Search

Bu çalışmada; bir halkanın terslenebilir olması kavramı, o halka üzerine kurulan skew Hurwitz polinomlar halkasına genişletilerek, zayıf skew Hurwitz terslenebilir (kısaca zayıf SH-terslenebilir) halka kavramı tanıtılmıştır. Bu halka sınıfının bazı özelikleri ve diğer halka sınıflarıyla ilişkileri incelenmiştir. Zayıf SH-terslenebilir halkaların bazı genişlemelerinin de zayıf SH-terslenebilir olup olmadığı araştırılmıştır. Özel olarak, karakteristiği 0 olan bir R halkası ve R’nin bir α monomorfizması için R’nin zayıf SH-terslenebilir olması için gerek ve yeter koşul A(R,α) Jordan genişlemesinin zayıf SH-terslenebilir olması gerektiği ispatlanmıştır., In this paper; the concept of the ability of a ring to be reversible is extended to the ring of skew Hurwitz polynomials established on that ring, and the concept of the weak skew Hurwitz reversible (briefly weak SH-reversible) ring is introduced. Some properties of this ring class and its relations with other ring classes are examined. It is also investigated whether some extension of weak SH-reversible rings are weak SH-reversible. In particular, it is proved that for a ring R with characteristic 0 and an α monomorphism of R the Jordan extension A (R, α) of R is weak SH-reversible if and only if R is weak SH-reversible.

For an endomorphism of a ring , the endomorphism is called left semicommutative if implies ( )semicommutative endomorphism of . In this paper, varios results of semicommutative rings are extended to left −semicommutative rings, bir halka ve da nin bir endomorfizması olmak üzere eğer, , ∈ için = 0 olması ( )= 0 olmasını gerektiriyor ise, bu durumda endomorfizmasına soldan yarıdeğişmelidir denir. Eğer bir halkasının soldan yarıdeğişmeli bir endomorfizması varsa, bu durumda halkasına soldan −yarıdeğişmeli halka denir. Bu çalışmada yarıdeğişmeli halkalar için bilinen bir çok sonuç soldan −yarıdeğişmeli halkalara genelleştirilecektir

This paper introduces and studies (X,Y)-Gorenstein projective and injective modules, which are a generalization of Enochs' Gorenstein projective and injective modules, respectively. Our main aim is to investigate the relations among various (X,Y)-Gorenstein projective modules.

In this paper, we introduce and study V -Gorenstein at modules and show the stability of the category of V -Gorenstein at modules. We investigate the existence of V -Gorenstein at covers and V -Gorenstein at preenvelopes for any left R -module. Also we prove that ( V - GF ;V - GF ? ) is a perfect hereditary cotorsion pair in B l ( R) , where V - GF stands the class of V -Gorenstein at left R -modules and B l ( R) is the left Bass class. Some applications are given.

In this paper, we introduce and study Ext-strongly Gorenstein projective modules. We prove that the class of Ext-strongly Gorenstein projective modules is projective resolving. Moreover, we consider Ext-strongly Gorenstein projective precovers.

In this paper we have obtained the following results for a differential ring (associative or nonassociative): (1) For a differential ring ({\cal D}-ring) we introduce definitions of a {\cal D}-prime {\cal D}-ideal, {\cal D}-semiprime {\cal D}-ideal and a strongly {\cal D}-nilpotent element. We define the {\cal D}-prime radical as the intersection of all {\cal D}-prime {\cal D}-ideals. For any {\cal D}-ring the {\cal D}-prime radical, the intersection of all {\cal D}-semiprime {\cal D}-semiprime {\cal D}-ideals and the set of all strongly {\cal D}-nilpotent elements are equal. (2) For a {\cal D}-ring we introduce a definition of an s-nilpotent {\cal D}-ideal. If a {\cal D}-ring satisfies the ascending chain condition for {\cal D}-ideals then its {\cal D}-prime radical is s-nilpotent. (3) Let {\cal Q} be a field of rational numbers. If d is a differentiation of a {\cal Q}-algebra R with 1 then d (Pr.rad(R))\subseteq Pr. rad(R). (4) Let K be a differential ring. Then every radical {\cal D}-ideal of K is an intersection of {\cal D}-prime {\cal D}-ideals.

This paper is concerned with a method based on birational geometry and produces dozens of new examples in codimensions 3, 4, 5 etc. The method is called unprojection by Reid. Using this method we construct new examples of K3 surfaces of codimensions 3 and 4 in weighted projective spaces from smaller codimension K3 surfaces whose rings are much simpler. This leads to the existence of almost all candidates for codimension 3 K3 surfaces in the list.

In tins paper, we give some characterizations of modules M over a ring R such that every submodule has a unique closure relative to a hereditary torsion theory on Mod- R by using the concept of tau-closed submodule which was studied in [2]. We compare UC and tau-UC modules and examine the relationships between them. We also give some examples of tau-UC and UC modules and submodules which have a unique tau-closure and unique closure.

In this paper, we study quadric surfaces in a Euclidean 3-space. Furthermore, we classify quadric surfaces in a Euclidean 3-space in terms of the Gaussian curvature and the mean curvature.

In this paper we call a ring R delta(r)-clean if every element is the sum of an idempotent and an element in delta(R-R) where delta(R-R) is the intersection of all essential maximal right ideals of R. If this representation is unique (and the elements commute) for every element we call the ring uniquely (strongly) delta(r)-clean. Various basic characterizations and properties of these rings are proved, and many extensions are investigated and many examples are given. In particular, we see that the class of delta(r)-clean rings lies between the class of uniquely clean rings and the class of exchange rings, and the class of uniquely strongly delta(r)-clean rings is a subclass of the class of uniquely strongly clean rings. We prove that R is delta(r)-clean if and only if R/delta(r)(R-R) is Boolean and R/Soc(R-R) is clean where Soc(R-R) is the right socle of R.

Let R be a commutative ring with a unit and M an R-module. In this paper we give a comparison between the F-closure in M of an R-submodule having a minimal extension and the closure of this minimal extension for the same Gabriel topology defined on the ring R. If J(R) \in F we prove that both closures are the same. Moreover, if R is Artinian or semi-simple then the converse also holds.

The aim of this paper is to introduce the notion of fuzzy left (resp. right) ideals of G-near-rings, and to study the related properties.

In ring theory, it is shown that a commutative ring R with Krull dimension has classical Krull dimension and satisfies k.dim(R)=cl.k.dim(R). Moreover, R has only a finite number of distinct minimal prime ideals and some finite product of the minimal primes is zero (see Gordon and Robson [9, Theorem 8.12, Corollary 8.14, and Proposition 7.3]). In this paper, we give a generalization of these facts for multiplication modules over commutative rings. Actually, among other results, we prove that if M is a multiplication R-module with Krull dimension, then: (i) M is finitely generated, (ii) R has finitely many minimal prime ideals P1, ..., Pn of Ann(M) such that P1k...PnkM=(0) for some k \geq 1, and (iii) M has classical Krull dimension and k.dim(M)=cl.k.dim(M)=k.dim(M/PM)= cl.k.dim(M/PM) for some prime ideal P of R.

A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

In this paper, we discuss the Bass class and the Auslander class with respect to a semidualizing module over an associative ring. Let SCR be a semidualizing module, we proved that the Bass class BC (R) is a right orthogonal subcategory of some right R-module; and that the Auslander class AC (S) is a left orthogonal subcategory of the character module of some left S-module. As an application, we introduce the notion of the minimal semidualizing module, and get a one to one correspondence between the isomorphism classes of minimal semidualizing R-modules and maximal classes among coresolving preenvelope classes of Mod R with the same Ext-projective generators in gen* R.

In this paper, we introduce some characterizations for augmented graded rings in special cases.

In this paper, the authors prove that every representable module over a commutative ring with identity satisfies the radical formula. With this result, they extend the class of modules satisfying the radical formula from that of Artinian modules to a larger one. They conclude their work by giving a description of the radical of a submodule of a representable module.

Let G be a multiplicative group with identity e, and let R be an associative G-graded ring with unity 1. In this paper we study the augmented graded Noetherian modules and try to give some relationships between the Noetherian modules in the category R-Agr and the Noetherian modules in the category Re-gr.

In this paper we consider the product of all elements in the group of units in a finite ring and we generalize Wilson's theorem to finite rings. As an application, we study some generalizations of Wilson's theorem on residually finite Dedekind domains. And we also give some examples for such rings. Moreover we study some generalizations of Wilson's theorem on rings of matrices over a finite commutative ring.

WOS: 000283892900008, The aim of this paper is to define a new kind of fuzzy gamma ring. So the concepts of fuzzy gamma ring, fuzzy ideal, fuzzy quotient gamma ring, and fuzzy gamma homomorphism are introduced.

In this paper, we introduce the concept of normal ideal of a subtractionalgebra and study properties in connection with multiplies of subtraction algebras. The image and inverse image of a normal ideal of a subtraction algebra are proved to be again normal ideals. Also, we characterize the normal ideals of direct products of subtraction algebras.Finally, the concept of a weak congruence is introduced in subtractionalgebras and obtain an interconnection between multipliers and weakcongruences.