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In ring theory, duoness and Zhou radical which is known as delta ideal have important roles. In this paper, we consider both concepts together by studying duoness on Zhou radical. By means of this study, we obtain a new kind of generalizations of commutativity. Firstly, we determine Zhou radical of some rings, then Zhou radical is applied to the duo property of rings, so we introduce a notion of right (left) dZr rings. We show that this notion is not left-right symmetric. We investigate some relations between right dZr rings and certain rings, and also deal with some ring extensions in terms of dZr property.

Ahmet Hamdi Tanpınar who provided works in different genres of the literature had been seeking for the quite gnomic and efficacious pronunciation almost in all his works. His pronunciation inclined to aphorism and based on intensive weight of ideas borne by concise and conspicuous sentences has been a part of Tanpınar’s style. Şerif Oktürk reviewed the works of Tanpınar from 1977 and published sentences of author having features of epigrams into a book titled Thoughts, Opinions and Epigraphs from Tanpınar (1977). Book includes “1170 ideas in 185 topics”. It is seen that many different subjects have been treated in these epigrams of Ahmet Hamdi Tanpınar that spread the works in different forms such as novel, short story, essay, letter, article and journal and compiled by Şerif Oktürk. In the main subjects, followings can be considered; pain, name, tree, moral, family, mind, garden, start, science, to be fed up, boredom, geography, to work, child, resentment, to change, value, genius, mad, era, nature, night, youth, news, people, sincerity, woman, hero, machine, happiness, school, money, patience, imitation, nation, hope, land, Yahya Kemal, to write, author, to direct, time, intelligence, richness rtc. In this article, based on the compilation of Şerif Öztürk author’s use feature of epigrammatic expression that effected different genres of works have been examined, and following question has been attempted to be answered; mainly in which topics Tanpınar expressed his ideas; ideas he expressed in different topics have been summarized and reasons of the impressions left by his language and style on reader have been attempted to be understood.

Selim İleri, Cumhuriyet dönemi öykü ve romancılığımızın üretken isimlerindendir. Bu türler dışında da, deneme, inceleme, anı, tiyatro, senaryo, şiir türlerinde eserler vermiştir. Makalede, yazarın bütün eserlerinin genel bir değerlendirmesi yapıldıktan sonra, bütün bu eserleri domine eden ana yönelimler üzerinde durulmuştur. İlk öykülerinden itibaren Selim İleri’nin eserlerinin arka planında hüzün duygusu egemendir. Bu duygu, çoğunlukla yazdıklarının motivasyonu olmuştur. Aynı zamanda yazarın değişen dünyaya ve Türk toplumuna karşı eleştirel bir yaklaşım içinde olduğu, Abdülhak Şinasi Hisar’ın eserlerindeki gibi bir “güzel duygularla anımsanan bir mazi” inşa etmeye çalıştığı söylenebilir. Yaşanmakta olan değişime karşı içte beslenen muhalefet duygusunun çeşitlemeleri yazarın pek çok türde verdiği eserlerine bir biçimde yansımıştır. Yaşadığı zamandan memnun olmayan yazarın aradığı mutluluğu olumsuzluklarından arındırılmış bir geçmiş zaman diliminde bulmak istemesi de belki bir anlamda kendini mutlu ve huzurlu kılma yoludur.

An ideal $I$ of a ring $R$ is called left N-reflexive if for any $a\in$ nil$(R)$, $b\in R$, being $aRb \subseteq I$ implies $bRa \subseteq I$ where nil$(R)$ is the set of all nilpotent elements of $R$. The ring $R$ is called left N-reflexive if the zero ideal is left N-reflexive. We study the properties of left N-reflexive rings and related concepts. Since reflexive rings and reduced rings are left N-reflexive, we investigate the sufficient conditions for left N-reflexive rings to be reflexive and reduced. We first consider basic extensions of left N-reflexive rings. For an ideal-symmetric ideal $I$ of a ring $R$, $R/I$ is left N-reflexive. If an ideal $I$ of a ring $R$ is reduced as a ring without identity and $R/I$ is left N-reflexive, then $R$ is left N-reflexive. If $R$ is a quasi-Armendariz ring and the coefficients of any nilpotent polynomial in $R[x]$ are nilpotent in $R$, it is proved that $R$ is left N-reflexive if and only if $R[x]$ is left N-reflexive. We show that the concept of N-reflexivity is weaker than that of reflexivity and stronger than that of left N-right idempotent reflexivity and right idempotent reflexivity which are introduced in Section 5.

In this paper we introduce the concepts of $CD$-rings and $CD$-modules. Let $R$ be a ring and $M$ be an $R$-module. We call $R$ a $CD$-ring in case every cosingular $R$-module is discrete, and $M$ a $CD$-module if every $M$-cosingular $R$-module in $\sigma[M]$ is discrete. If $R$ is a ring such that the class of cosingular $R$-modules is closed under factor modules, then it is proved that $R$ is a $CD$-ring if and only if every cosingular $R$-module is semisimple. The relations of $CD$-rings are investigated with $V$-rings, $GV$-rings, $SC$-rings, and rings with all cosingular $R$-modules projective. If $R$ is a semilocal ring, then it is shown that $R$ is right $CD$ if and only if $R$ is left $SC$ with $Soc(_{R}R)$ essential in $_{R}R$. Also, being a $V$-ring and being a $CD$-ring coincide for local rings. Besides of these, we characterize $CD$-modules with finite hollow dimension.

Let M n ( F ) be the set of all n × n matrices over the field F , where F = R or F = C . We characterize maps on M n ( F ) which are surjective and preserve either the left-star or the right-star order in both directions, but are not necessarily additive.

The purpose of this paper is to determine exactly the shorted operators in the sense of linear functionals under the direct sum partial order.

We investigate properties of the minus partial order in regular modules, present new characterizations of this order, and generalize some known results. We introduce a new relation in the general module theoretic setting that is analogous to the space pre-order on complex matrices and study how it is related to the minus partial order.

In this paper, information about lives and works of some poets and authors born in Aksaray who provided some works in various literal genres in Republican Period Turkish Literature is given, and also literal personality of said man of letters are assessed. We think that such micro-size works shall simplify understanding of “center” –“country” concepts and relationships of these concepts with each other. Our purpose is to determine poets and authors of Aksaray city, on the one hand, and attempt to understand to which point did center-country conflicts come in Turkish literature today, on the other hand. There are some poets and authors from Aksaray in the Turkish Literature of the Republic Period such as Nusret Kemal Otyam, Fikret Otyam, Mahmut Makal, Nahit Eruz, Ülkü Uluırmak, Hayrettin Ökçesiz, Zeynep Ankara, Ali Ekecik, Mehmet Can Doğan who took place in the main movement of our modern literature by providing some works in general media organs which made tremendous impact across the country, as well as, those who attempted to make their name by benefiting from local media opportunities such as Gökmen Yılmaz Erdem, Hasan Tosun, Latif Sarı, Yaşar Akbaş, Akın Akbulut, İbrahim Amaç, Hüseyin Sarıkaya, Mustafa Birgin, Fatih Coşkun, Mustafa Erdem Özçiftçi, Yavuz Bal, Çiğdem Çakır, İshak Pekgöz, Yalçın Sevindi, Sinan Uğurlu, Celaleddin Satılmış, Ali Öztürk, Hasan Eskil, Şahin Kulaksız, Ramazan Solak, Yakup Zengin, Veli Demir, Yavuz Bayram Çalışkan, Ahmet Aytaç.

Arif Ay who entered into the world of literature with the journal Edebiyat (Literature) directed by Nuri Pakdil published his first poetry book “Hıra” in 1978. Arif Ay who published many poetry books and deepened and enriched his poetry compiled his poetries in 2006 with his book titled Güne Doğan Koşu . Poet who did not ignore emotional world of the in

5th International Conference Noncommutative Rings and their Applications -- JUN 12-15, 2017 -- Univ Artois, Lens, FRANCE WOS: 000473290900019 In this paper, we deal with some versions of reversibility and symmetricity on amalgamated rings along an ideal. Ahi Evran University Scientific Research Projects Coordination UnitAhi Evran University [FEF.A4.16.001] The first author was supported by Ahi Evran University Scientific Research Projects Coordination Unit. Project Number: FEF.A4.16.001.

A ring R is defined to be J-normal if for any $$a, r\in R$$ and idempotent $$e\in R$$, $$ae = 0$$ implies $$Rera\subseteq J(R)$$, where J(R) is the Jacobson radical of R. The class of J-normal rings lies between the classes of weakly normal rings and left min-abel rings. It is proved that R is J-normal if and only if for any idempotent $$e\in R$$ and for any $$r\in R$$, $$R(1 - e)re\subseteq J(R)$$ if and only if for any $$n\ge 1$$, the $$n\times n$$ upper triangular matrix ring $$U_{n}(R)$$ is a J-normal ring if and only if the Dorroh extension of R by $${\mathbb {Z}}$$ is J-normal. We show that R is strongly regular if and only if R is J-normal and von Neumann regular. For a J-normal ring R, it is obtained that R is clean if and only if R is exchange. We also investigate J-normality of certain subrings of the ring of $$2\times 2$$ matrices over R.

In this paper, we focus on the duo ring property via quasinilpotent elements, which gives a new kind of generalizations of commutativity. We call this kind of rings qnil-duo. Firstly, some properties of quasinilpotents in a ring are provided. Then the set of quasinilpotents is applied to the duo property of rings, in this perspective, we introduce and study right (resp., left) qnil-duo rings. We show that this concept is not left-right symmetric. Among others, it is proved that if the Hurwitz series ring $H(R; \alpha)$ is right qnil-duo, then $R$ is right qnil-duo. Every right qnil-duo ring is abelian. A right qnil-duo exchange ring has stable range 1.

Let R be a ring with identity, M be a right R-module and F be a fully invariant submodule of M. The concept of an F-inverse split module M has been investigated recently. In this paper, we approach to this concept with a different perspective, that is, we deal with a notion of an F-image split module M, and study various properties and obtain some characterizations of this kind of modules. By means of F-image split modules M, we focus on modules M in which fully invariant submodules F are dual Rickart direct summands. In this way, we contribute to the notion of a T-dual Rickart module M by considering Z?2 (M) as the fully invariant submodule F of M. We also deal with a notion of relatively image splitness to investigate direct sums of image split modules. Some applications of image split modules to rings are given.

Regarding the question of how idempotent elements affect the reversible property of rings, we study a version of reversibility depending on idempotents. In this perspective, we introduce right (resp., left) 𝑒-reversible rings. We show that this concept is not left-right symmetric. Basic properties of right 𝑒-reversibility in a ring are provided. Among others, it is proved that if 𝑅 is a semiprime ring, then 𝑅 is right 𝑒-reversible if and only if it is right 𝑒-reduced if and only if it is 𝑒-symmetric if and only if it is right 𝑒-semicommutative. Also, for a right 𝑒-reversible ring 𝑅, 𝑅 is a prime ring if and only if it is a domain. It is shown that the class of right 𝑒-reversible rings lies strictly between that of 𝑒-symmetric rings and right 𝑒-semicommutative rings. Some extensions of rings are studied in terms of 𝑒-reversibility.

Grandfather is a factor that affects a person's life from different points of view. If a person considers himself as a result, it would not be wrong to think that the grandfather would be the cause of many things. It is unimaginable that an actor who has such a great impact on people and his life would not be reflected in the literature produced by humans in different ways. In modern Turkish literature, it is seen that the grandfather is mentioned in many literary genres and fields extending from poetry to short story, novel and children's literature.Modern life changes everything, as well as the grandfather. The positive relationships between grandchildren and grandparents change within the challenges of modern life. Grandfather was sometimes the matter of change and moved away from his family. Being without a grandfather has been the subject of many essays and short stories, poems. In the article, it will be attempted to answer the question of how the grandfather figure is mentioned in adults' literature, especially in the genres of short stories and poetry, as well as in different genres of children's literature., Dede, bir insanın hayatında, birçok farklı açından onu etkileyen bir faktördür. İnsan kendini bir sonuç olarak görmekteyse, dedenin birçok şeyin sebebi olduğunu düşünmek yanlış olmaz. İnsana ve onun hayatına böylesine büyük etkisi olan bir aktörün gene insan tarafından üretilen edebiyata farklı biçimlerde yansımaması düşünülemez. Modern Türk edebiyatında şiirden öyküye, romana ve çocuk edebiyatına uzanan birçok edebi türde ve alanda dedenin konu edildiği görülür. Modern hayat her şeyi değiştirdiği gibi dedeyi de değiştirir. Torunla dedenin arasındaki olumlu ilişkiler, modern hayatın zorunlulukları içerisinde değişir. Dede bazen değişimin konusu olmuş ve ailesinden uzaklaşmıştır. Dedesiz olmak, birçok yazının ve öykünün, şiirin konusu haline getirilmiştir. Makalede; yetişkin edebiyatında özellikle öykü ve şiir türlerinde, ayrıca çocuk edebiyatının farklı türlerinde dede figürünün nasıl ele alındığı sorusu cevaplandırılmaya çalışılacaktır.

ARis the sum of a unit and a projection that commute with each other. Inthis paper, we explore strong -cleanness of rings of continuous functions overspectrum spaces. We prove that a -ring R is strongly -clean if and only if Ris an abelian exchange ring and C(X) C (X) is-clean, if and only if R isan abelian exchange ring and the classical ring of quotients q(C(X)) of C(X)is -clean, where X is a spectrum space of R

The minus partial order is already known for sets of matrices over a field and bounded linear operators on arbitrary Hilbert spaces. Recently, this partial order has been studied on Rickart rings. In this paper, we extend the concept of the minus relation to the module theoretic setting and prove that this relation is a partial order when the module is regular. Moreover, various characterizations of the minus partial order in regular modules are presented and some well-known results are also generalized., 15 pages

In this paper, we focus on the semicommutative property of rings via idempotent elements. In this direction, we introduce a class of rings, so-called right e-semicommutative rings. The notion of right e-semicommutative rings generalizes those of semicommutative rings, e-symmetric rings and right e-reduced rings. We present examples of right e-semicommutative rings that are neither semicommutative nor e-symmetric nor right e-reduced. Some extensions of rings such as Dorroh extensions and some subrings of matrix rings are investigated in terms of right e-semicommutativity. We prove that if R is a right e-semicommutative clean ring, then the corner ring eRe is clean. © 2019, University of Nis. All rights reserved.

In this paper, we introduce a concept of a dual F-Baer module M where F is the fully invariant submodule of M, by this means we deal with generating dual Baer modules. We investigate direct sums of dual F-Baer modules M by exerting the notion of relatively dual F-Baer modules. We also obtain applications of dual F-Baer modules to rings and the preradical Z * (.).Mathematics Subject Classification (2010): 16D10, 16D40, 16D70, 16D80.Keywords: Dual Baer module, dual inverse split module, fully invariant submodule, cosingular submodule

In this paper, we deal with a new approach to quasipolarity notion for rings, namely an element a of a ring R is called weakly nil-quasipolar if there exists \(p^2 = p\in comm^2(a)\) such that \(a + p\) or \(a-p\) is nilpotent, and the ring R is called weakly nil-quasipolar if every element of R is weakly nil-quasipolar. The class of weakly nil-quasipolar rings lies properly between the classes of nil-quasipolar rings and quasipolar rings. Although it is an open problem whether strongly clean (even quasipolar) rings have stable range one, we show that there is an affirmative answer for weakly nil-quasipolar rings. It is also proved that if R is a weakly nil-quasipolar NI ring, then R / N(R) is commutative. Moreover, we consider the question of when certain \(2 \times 2\) matrices over a commutative local ring is weakly nil-quasipolar.

Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). Let F be a fully invariant submodule of M. We call M an F-inverse split module if f−1(F) is a direct summand of M for every f ∈ S. This work is devoted to investigation of various properties and characterizations of an F-inverse split module M and to show, among others, the following results: (1) the module M is F-inverse split if and only if M = F ⊕ K where K is a Rickart module; (2) for every free R-module M, there exists a fully invariant submodule F of M such that M is F-inverse split if and only if for every projective R-module M, there exists a fully invariant submodule F of M such that M is F-inverse split; and (3) Every R-module M is Z2(M)-inverse split and Z2(M) is projective if and only if R is semisimple.

The class of $H$-supplemented modules, which is a nice generalization of that of lifting modules, has been studied extensively in the last decade. As the concept of homomorphisms plays an important role in module theory, we are interested in $H$-supplemented modules relative to homomorphisms. Let $R$ be a ring, $M$ a right $R$-module, and $S=$ End$_{R}(M)$. We say that $M$ is endomorphism $H$-supplemented (briefly, $E$-$H$-supplemented) provided that for every $f\in S$ there exists a direct summand $D$ of $M$ such that $Imf+X=M$ if and only if $D+X=M$ for every submodule $X$ of $M$. In this paper, we deal with the $E$-$H$-supplemented property of modules and also a similar property for a module $M$ by considering Hom$_R(N,M)$ instead of $S$ where $N$ is any module.

In this paper, we define the direct sum relation on a module and prove that this is a partial order when the module is regular. We also focus on a regular support and a strong regular support of an element in a module, which are extensions of a generalized inverse and a reflexive generalized inverse of an element in a ring, respectively. Using regular supports and strong regular supports, we present various characterizations of the direct sum order as an application. We obtain some decompositions of a module via the direct sum order.

Let $R$ be a ring and $M$ be an $R$-module. In this paper we investigate modules $M$ such that every (simple) cosingular $R$-module is $M$-projective. We prove that every simple cosingular module is $M$-projective if and only if for $N\leq T\leq M$, whenever $T/N$ is simple cosingular, then $N$ is a direct summand of $T$. We show that every simple cosingular right $R$-module is projective if and only if $R$ is a right $GV$-ring. It is also shown that for a right perfect ring $R$, every cosingular right $R$-module is projective if and only if $R$ is a right $GV$-ring. In addition, we prove that if every $\delta$-cosingular right $R$-module is semisimple, then $\overline{Z}(M)$ is a direct summand of $M$ for every right $R$-module $M$ if and only if $\overline{Z}_{\delta}(M)$ is a direct summand of $M$ for every right $R$-module $M$.

In this paper, we study on the primeness and semiprimeness of a Morita context related to the rings and modules. Necessary and sufficient conditions are investigated for an ideal of a Morita context to be a prime ideal and a semiprime ideal. In particular, we determine the conditions under which a Morita context is prime and semiprime.

Let R be a ring with identity and J(R) denote the Jacobson radical of R. A ring R is called J-reversible if for any a, $$b \in R$$ , $$ab = 0$$ implies $$ba \in J(R)$$ . In this paper, we give some properties of J-reversible rings. We prove that some results of reversible rings can be extended to J-reversible rings for this general setting. We show that J-quasipolar rings, local rings, semicommutative rings, central reversible rings and weakly reversible rings are J-reversible. As an application it is shown that every J-clean ring is directly finite.

Let R be an arbitrary ring with identity and M a right R-module with S= End(R)(M). Let F be a fully invariant submodule of M and I-1(F) denotes the set {m is an element of M : Im subset of F} for any subset I of S. The module M is called F-Baer if I-1(F) is a direct summand of M for every left ideal I of S. This work is devoted to the investigation of properties of F-Baer modules. We use F-Baer modules to decompose a module into two parts consists of a Baer module and a module determined by fully invariant submodule F, namely, for a module M, we show that M is F-Baer if and only if M = F circle plus N where N is a Baer module. By using F-Baer modules, we obtain some new results for Baer rings.

Let \(R\) be an arbitrary ring. An element \(a\in R\) is nil-quasipolar if there exists \(p^2=p\in comm^2(a)\) such that \(a+p\in Nil(R)\); \(R\) is called nil-quasipolar in case each of its elements is nil-quasipolar. In this paper, we study nil-quasipolar rings over commutative local rings. We determine the conditions under which a single \(2\times 2\) matrix over a commutative local ring is nil-quasipolar. It is shown that \(A\in M_2(R)\) is nil-quasipolar if and only if \(A\in Nil\big (M_2(R)\big )\) or \(A+I_2\in Nil\big (M_2(R)\big )\) or the characteristic polynomial \(\chi (A)\) has a root in \(Nil(R)\) and a root in \(-1+Nil(R)\). We give some equivalent characterizations of nil-quasipolar rings through the endomorphism ring of a module. Among others we prove that every nil-quasipolar ring has stable range one.

Let [Formula: see text] be a ring. Motivated by a generalization of a well-known minus partial order to Rickart rings, we introduce a new relation on the power set [Formula: see text] of [Formula: see text] and show that this relation, which we call “the minus order on [Formula: see text]”, is a partial order when [Formula: see text] is a Baer ring. We similarly introduce and study properties of the star, the left-star, and the right-star partial orders on the power sets of Baer ∗-rings. We show that some ideals generated by projections of a von Neumann regular and Baer ∗-ring [Formula: see text] form a lattice with respect to the star partial order on [Formula: see text]. As a particular case, we present characterizations of these orders on the power set of [Formula: see text], the algebra of all bounded linear operators on a Hilbert space [Formula: see text].

An element a of a ring R is called quasipolar provided that there exists an idempotent p ∈ R such that p ∈ comm2(a), a + p ∈ U (R) and ap ∈ Bqnil. A ring R is quasipolar in case every element in R is quasipolar. In this paper, we determine conditions under which subrings of 3 x 3 matrix rings over local rings are quasipolar. Namely, if R. is a bleached local ring, then we prove that T3 (R) is quasipolar if and only if R is uniquely bleached. Furthermore, it is shown that Tn(R) is quasipolar if and only if Tn(R[[x]]) is quasipolar for any positive integer

It is a fact that one of the most frequently referred methods to raise colloquial language and ordinary language to the literal and fictional language level and to expand literary text/poetry opportunities is “language deviations” Especially, since 1950s, it was started tobenefit from “language deviations” in our poetries that we may defineordinary language rules as writing, phonetic, word, expression,grammar, change in semantic levels. The Second New Poetry that hasbeen effective in our literature for some researchers between 1954 and1959 and for some researchers between 1953 and 1963 put the literaryarts, imaginative pronunciation, abstract language, closed-formexpression and language experience deliberatively ignored by the GaripPoetry Movement at forefront and pushed the limits of language. Heattempted to expand opportunities of Turkish, so largely benefited fromlinguistic deviations. Cemal Süreya who had been one of the importantrepresentatives of the Second Poetry applied these methods in hispoems. In this article, after the theoretical knowledge about the SecondNew Poetry and linguistic deviations, all the poems of Cemal Süreyawere reviewed and linguistic deviations we determined in poetries weresampled, and it was attempted to discuss why the poet needed thismethod, what kind of effects of linguistic deviations have been in hispoetry. Deviations used from the poetry of Cemal Süreya; wereattempted to be examined under seven titles; writing deviations,phonetic deviations, word deviations, grammar deviations,interventions to borrowed texts, meaning deviations or extraordinarysyncretism. Gündelik, ortalama dili; edebi, kurmaca dil seviyesine yükseltmek, edebî metnin/şiirin imkânlarını genişletmek amacıyla şair ve yazarlar tarafından sıkça başvurulan yöntemlerden birinin de “dil sapmaları” olduğu bir gerçektir. Dilin alışılmış kurallarını; yazım, ses, kelime, ifade, dilbilgisi, anlam düzeylerinde değiştirme, bozma şeklinde tanımlayabileceğimiz “dil sapmaları”ndan şiirimizde özellikle 1950’li senelerden itibaren yararlanılmaya başlanmıştır. Kimi araştırmacılara göre 1954 - 1959, kimi araştırmacılara göre ise 1953 – 1963 yılları arasında edebiyatımızda etkili olan İkinci Yeni şiiri, Garip şiir hareketinin bilinçli bir şekilde ihmal ettiği edebi sanatları, imgeli söyleyişleri, soyut dili, kapalı anlatım biçimlerini, dil deneylerini ön plana çıkarmış, dilin sınırlarını zorlamış, Türkçenin imkânlarını genişletmeye çalışmış, dolayısıyla da dil sapmalarından geniş oranda yararlanmıştır. İkinci Yeni şiirinin önemli temsilcilerinden olan Cemal Süreya da, bu yöntemleri şiirlerinde uygulamıştır. Bu makalede; İkinci Yeni şiiri ve dil sapmaları hakkında verilen teorik bilgilerin ardından, Cemal Süreya’nın tüm şiirleri taranmış, şiirlerde tespit edebildiğimiz dil sapmaları örneklenmiş ve onun şiirine dil sapmalarının ne gibi etkileri olduğu, şairin bu yönteme neden ihtiyaç duyduğu tartışılmaya çalışılmıştır. Cemal Süreya şiirinde yararlanılan sapmalar; yazım sapmaları, ses sapmaları, kelime sapmaları, dilbilgisi sapmaları, ödünç metinlere müdahaleler, anlam sapmaları ya da alışılmamış bağdaştırmalar olmak üzere yedi başlık altında incelenmeye gayret edilmiştir.

Ali Canip Yöntem (1887-1967) who is one of the prominent names of the national literary movement gave many works relating to literary theory and criticism as well as poem. Before being connected to national literary, author who has largely been seeking on the line extending from Muallim Naci to Cedideci (New Literature movement) and Fecr-i Aticis (Dawn of the Future) has deep thoughts in his many articles that will light the way for today’s artists and researchers either due to hiscommand of our classical literature or of Western Literature. From hiswritings in question, in our article, opinions of Yöntem about somematters such as what is the art and literature, why it is existing, whatcould be its power and effect, how to take advantage of art andliterature, the place and importance of the imitation in art, pleasure,beauty, perception and genius concepts, purpose of art, relationshipbetween artist and school of art, art and dialectic, poem and knowledge,poem and sensation etc were scanned and these opinions were whollyattempted to be assessed. Apart from these, problems collected undersome titles such as what, in fact, is the concept of national literature adhow it should be understood, our mistakes when assessing the concept“national”, dimensions of artist and public when assessing within thecontext of national literature have been the topic of the Ali CanipYöntem’s articles and opinions of author about these issues wereattempted to be examined by us. Yöntem also referred to the problemsabout limits of literary criticism and features which a reviewer musthave, and attached importance to the relationship of literary criticismwith literary text. Milli edebiyat akımının önde gelen isimlerinden olan Ali Canip Yöntem (1887 – 1967), şiirin yanı sıra edebiyat teorisine ve eleştirisine ilişkin eserler de vermiştir. Milli edebiyata mensup olmadan önce, Muallim Naci’den Edebiyatı Cedidecilere, Fecr-i Âticilere uzanan çizgide geniş bir arayış içinde olan yazar, yazdığı çok sayıdaki makalesinde, gerek dönemindeki Türk edebiyatına, gerekse klasik edebiyatımıza ve Batı edebiyatına hakimiyetiyle, günümüz sanatçı ve araştırmacılarına ışık tutacak derinlikli düşüncelere sahiptir. Makalemizde; söz konusu yazılarından hareketle, Yöntem’in; sanat ve edebiyatın ne olduğu, ne için var olduğu, gücünün ve etkisinin ne olabileceği, sanat ve edebiyattan nasıl yararlanılabileceği, sanatta taklit, haz, güzellik, sezgi, deha kavramlarının yeri ve önemi, sanatın gayesi, sanatçı – sanat mektebi ilişkisi, sanat ve diyalektik, şiir ve bilgi, şiir ve duygu gibi meselelerdeki görüşleri taranarak, bu düşünceleri bütünlüklü bir biçimde değerlendirilmeye çalışılmıştır. Bunların dışında, milli edebiyat kavramının gerçekte ne olduğu ve nasıl anlaşılması gerektiği, bizde “milli”lik kavramı değerlendirilirken yapılan hatalar, milli edebiyat bağlamında değerlendirildiğinde sanatçı – halk ilişkisinin boyutları gibi başlıklarda toplanabilecek problemler de Ali Canip Yöntem’in makalelerine konu olmuş ve tarafımızdan, yazarın bu meselelerdeki görüşleri incelenmeye çalışılmıştır. Yöntem, ayrıca, edebi eleştirinin sınırları ve eleştirmenin sahip olması gereken nitelikleri sorunlarına da değinmiş, edebi eleştirinin edebi metinle olan ilişkisini önemsemiştir.

Cihan Aktaş who is known by his books of thought and review as well as short stories published nine short story books between 1992 and 2009. The author, who refers to Azerbaijan and Azerbaijanis, especially in his short story book titled the Last Day of Azize (1997), either brought interesting portraits of Azerbaijani Turks in these texts or conveyed important information related to the culture, folklore, social and political life and economical conditions of Azerbaijan. He also narrated his impressions related to Azerbaijan geography and environmental area, especially to Baku. In this article, we will attempt to understand image/perception of Azerbaijan and Azerbaijanis reflecting on the book of Cihan AktaĢ titled “the Last Day of Azize”. Düşünce, inceleme kitaplarıyla olduğu kadar öyküleriyle de tanınan Cihan Aktaş, 1992 – 2009 yılları arasında dokuz öykü kitabı yayımlamıştır. Özellikle Azize’nin Son Günü (1997) adlı öykü kitabında olmak üzere, öykülerinde Azerbaycan’dan ve Azeri Türklerinden bahseden yazar, bu metinlerde gerek Azeri Türklerinden ilginç portreleri edebiyatımıza kazandırmakta, gerekse Azerbaycan kültürüyle, folkloruyla, sosyal ve siyasi hayatıyla, ekonomik Ģartlarıyla ilgili önemli bilgiler aktarmaktadır. Ayrıca baĢta Baku olmak üzere Azerbaycan coğrafyasına ve çevre bölgelere iliĢkin izlenimlerini öyküleĢtirmektedir. Bu makalede, Cihan AktaĢ’ın Azize’nin Son Günü adlı öykü kitabına yansıyan Azerbaycan ve Azeri Türkü imgesi/algısı incelenmeye çalışılacaktır.

Hüseyin Rahmi Gürpınar, one of the important authors of the New Turkish Literature, wrote a great number of works in some genres such as novel, short story, drama, letter, critiques etc. Gürpınar who came to the forefront mostly with his novels made important contributions to our storytelling with his nine short story books both in the sense of quality and quantity. It is seen in short stories of Gürpınar that social critique came to the forefront as well as in his other works. Author who assumed a critical attitude toward from state administrators to our public and from religious functionaries to moral disintegration ,sometimes expressed his critiques directly and sometimes presented within the dramatic expression of short story, but more indirectly. Yeni Türk Edebiyatının önemli yazarlarından olan Hüseyin Rahmi Gürpınar; roman, öykü, piyes, mektup, eleştiri gibi türlerde çok sayıda eser vermiştir. Daha çok romanlarıyla ön plana çıkmış olan Gürpınar, yayınladığı dokuz öykü kitabıyla, hem nitelik hem de nicelik anlamında öykücülüğümüze de önemli katkılarda bulunmuştur. Gürpınar’ın diğer eserlerinde olduğu gibi öykülerinde de toplumsal eleştirinin ön plana çıktığı görülmektedir. Devleti idare edenlerden halkımıza, din adamlarından toplumdaki ahlaki çözülmeye kadar pek çok alanda eleştirel bir tavır takınan yazar, eleştirilerini zaman zaman doğrudan dile getirmekte, zaman zaman öykünün dramatik anlatımı içinde daha dolaylı olarak sunmaktadır.

Let [Formula: see text] be an arbitrary ring with identity, [Formula: see text] a right [Formula: see text]-module and [Formula: see text] a fully invariant submodule of [Formula: see text]. The notion of an [Formula: see text]-inverse split module [Formula: see text] has been defined and studied by the present authors recently. In this paper, we introduce its dual notion, namely, dual [Formula: see text]-inverse split module [Formula: see text]. This work is devoted to investigation of various properties and characterizations of a dual [Formula: see text]-inverse split module [Formula: see text]. We include applications for rings and cosingular submodules. We also deal with the notion of relatively dual inverse splitness to investigate direct sums of dual inverse split modules.

It is seen that the “Kızılelma” motif that found an area of use in different genres of our traditional literature continues to make new senses in the Modern Turkish Literature with the pens of authors and poets such as Ziya Gökalp, Aka Gündüz, Ömer Seyfettin, Nihal Atsız, Niyazi Yıldırım Gençosmanoğlu, Dilaver Cebeci, Ragıp Şevki Yeşim, Mim Kemal Öke, Halil Delice. In our article, it’s attempted to introduce and assess these works and discussed new senses made by “Kızılelma” in our traditional and modern literature. Geleneksel edebiyatımızın farklı türlerinde kullanım alanı bulan “Kızılelma” motifinin, Yeni Türk Edebiyatında, Ziya Gökalp, Aka Gündüz, Ömer Seyfettin, Nihal Atsız, Niyazi Yıldırım Gençosmanoğlu, Dilaver Cebeci, Ragıp Şevki Yeşim, Mim Kemal Öke, Halil Delice gibi şair ve yazarların kaleminde yeni anlamlar kazanmaya devam ettiği görülmektedir. Makalemizde bu eserler tanıtılmaya ve değerlendirilmeye gayret edilmiş, “Kızılelma”nın geleneksel ve modern edebiyatımız içerisinde kazandığı anlamlar üzeride durulmuştur.

We consider when a single submodule and also when every submodule of a module M over a general ring R has a unique closure with respect to a hereditary torsion theory on Mod-R.

Short story that is one of the most importanttypes of Turkish Literature started to rise qualitatively and quantitatively especially by the 1990s and type of short story was greatly shown interest by our authors. With Adam Öykü Journal, publications have been made approximately for ten years and during fifty-eight editions between years 1995 – 2005, achieved great success to gain young authors in our literature and published considerable translations in the theory of short story that was a lack especially in Turkish. Bibliography of Adam Öykü that is as worthy as a treasure for short-story writers, short story readers and researchers shall ease the utilization from journal. Edebiyatımızın önemli türleri arasında yer alan öykü, 1990’larla niteliksel ve niceliksel anlamda yükselmeye başlamış, yazarlar tarafından öykü türüne büyük bir ilgi gösterilmiştir. Adam Öykü dergisi, 1995 – 2005 yılları arasında, yaklaşık on yıl süren elli sekiz sayılık yayaın hayatında, edebiyatımızda büyük eksikliği görülen öykü teorisi alanında kayda değer çeviriler yayımlamış ve edebiyatımıza genç öykücüler kazandırmayı başarmıştır. Bu bibliyografya çalışması, öykücüler, öykü okurları ve araştırmacılarımızın, bir hazine değerinde olan Adam Öykü’den yararlanmalarını kolaylaştıracaktır.

For an endomorphism of R, in (1), a module MR is called -compatible if, for any m 2 M and a 2 R, ma = 0 i m (a) = 0, which are a generalization of -reduced modules. We study on the relationship between the quasi-Baerness and p.q.- Baer property of a module MR and those of the polynomial extensions (including formal skew power series, skew Laurent polynomials and skew Laurent series). As a consequence we obtain a generalization of (2) and some results in (9). In particular, we show: for an -compatible module MR (1) MR is p.q.-Baer module i M(x; )R(x; ) is p.q.-Baer module. (2) for an automorphism of R, MR is p.q.-Baer module i M(x,x 1 ; )R(x,x 1; ) is p.q.- Baer module.

Let R be a ring with identity, M a right R-module and S = EndR(M). In this note, we introduce S-semicommutative, S-Baer, S-q.-Baer and S-p.q.-Baer modules. We study the relations between these classes of modules. Also we prove if M is an S-semicommutative module, then M is an S-p.q.-Baer module if and only if M[x] is an S[x]-p.q.-Baer module, M is an S-Baer module if and only if M[x] is an S[x]-Baer module, M is an S-q.-Baer module if and only if M[x] is an S[x]-q.-Baer module.

In this paper, we study a module which is lifting and supplemented relative to a module class. Let R be a ring, and let X be a class of R-modules. We will define X-lifting modules and X-supplemented modules. Several properties of these modules are proved. We also obtain results for the case of specific classes of modules.

In this paper, we introduce a kind of quasipolarity notion for rings, namely, an element a of a ring R is called central quasipolar if there exists p² = p ∈ R such that a+p is central in R, and the ring R is called central quasipolar if every element of R is central quasipolar. We give many characterizations and investigate general properties of central quasipolar rings. We determine the conditions that some subrings of upper triangular matrix rings are central quasipolar. A diagonal matrix over a local ring is characterized in terms of being central quasipolar. We prove that the class of central quasipolar rings lies between the classes of commutative rings and Dedekind finite rings, and a ring R is central quasipolar if and only if it is central clean. Further we show that several results of quasipolar rings can be extended to central quasipolar rings in this general setting. Resumen En este trabajo, se presenta una noción de un tipo de casi-polaridad en anillos, esto es, un elemento a de un anillo R se dice casi-polar central si existe p² = p ∈ R tal que a + p es central en R, y el anillo R es llamado casi-polar central si todo elemento de R es casi-polar central. Se dan algunas caracterizaciones y se investigan propiedades generales de los anillos centrales casi-polares. Se determinan las condiciones bajo las cuales algunos subanillos de anillos de matrices triangulares superiores son casi-polares centrales. Una matriz diagonal sobre un anillo local se caracteriza en términos de ser casi-polar central. Se demuestra que la clase de anillos casi-polares centrales se encuentra dentro de la clase de los anillos conmutativos y los anillos finitos de Dedekind, y un anillo R es casi-polar central si es limpio central. Además se muestra que varios resultados de anillos casi-polares se pueden extender a anillos casi-polares centrales en un contexto general.