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In 2011 M. Macaj and M. Sleziak first introduced the concept of IK convergence mainly as a generalization of statistical convergence. In this paper, we introduce and investigate a few interesting properties of IK convergence of real sequences. We also study some implication relations between I, I*, and IK-convergence of such sequences. Further, we find the conditions under which (i) IK-convergence implies K-convergence, (ii) IK-convergence implies I-convergence, (iii) I-convergence implies IK-convergence, and (iv) KI-convergence implies IK-convergence. [ABSTRACT FROM AUTHOR]

Let $$R$$ be a ring. A map $$F{:}R\rightarrow R$$ is called a multiplicative (generalized)-derivation if $$F(xy)=F(x)y+xg(y)$$ is fulfilled for all $$x,y\in R,$$ where $$g{:}R\rightarrow R$$ is any map (not necessarily a derivation). The main purpose of this paper is to study the following situations: (1) $$F([x,y])=\pm (xy\pm yx)$$ , (2) $$F(x\circ y)=\pm (xy\pm yx)$$ , (3) $$[F(x),y]\pm [x,G(y)]=0$$ , (4) $$F(uv)\pm uv=0$$ , (5) $$F(uv)\pm vu=0$$ , (6) $$F(u)F(v)\pm uv=0$$ , (7) $$F(u)F(v)\pm vu=0$$ , (8) $$F(uv)=F(u)F(v)$$ , (9) $$F(uv)=F(v)F(u)$$ for all $$x,y,u,v$$ in some appropriate subsets of $$R$$ . [ABSTRACT FROM AUTHOR]

The aim of this paper is to shed new light on an ethos of the subject as psychoanalysis conceives it. In order to do so, the paper is addressing Marc Richir's phenomenology and Jacques Lacan's psychoanalysis. The hypothesis that it makes use of is that there are some common grounds between the two theoretical approaches, especially regarding the problem of the self. Both theories support the idea that the self, i.e. self-image, represents a liminal point between the registers of the Imaginary and the Real. Thus, it represents a decisive point in approaching (or not) an ethics of the Real, facilitated by anguish and language. [ABSTRACT FROM AUTHOR]

Over the last few years, numerous researchers have contributed significantly to summability theory by connecting various notions of convergence concepts of sequences. In this paper, we introduce the concepts of ℐ -statistical supremum and ℐ -statistical infimum of a real-valued sequence and study some fundamental features of the newly introduced notions. We also introduce the concept of ℐ -statistical monotonicity and establish the condition under which an ℐ -statistical monotonic sequence is ℐ -statistical convergent. We end up giving a necessary and a sufficient condition for the ℐ -statistical convergence of a real-valued sequence. [ABSTRACT FROM AUTHOR]

A constructive procedure is given to determine all ideals of a finite-dimensional solvable Lie algebra. This is used in determining all conjugacy classes of subalgebras of a given finite-dimensional solvable Lie algebra. [ABSTRACT FROM AUTHOR]

In this paper, we characterize residuated lattices for which the topological space of prime ideals is a Noetherian space. The notion of i-Noetherian residuated lattice is introduced and related properties are investigated. We proved that a residuated lattice is i-Noetherian iff every ideal is principal. Moreover, we show that a residuated lattice has the spectrum of a Noetherian space iff it is i-Noetherian. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to reintroduce and study the concept of derivation on hyperlattices. We introduce the notion of joinitive and strong-joinitive derivation and study some of their properties and relationship with isotone and contractive derivations on hyperlattices. Moreover, we study some properties of the fixed set of principal derivation and investigate the relationship between prime ideals and derivations in hyperlattice. Finally, we prove that the set of all principal derivations on a bounded hyperlattice L is isomorphic to L and we investigate the structure of the set of fixed set of principal derivations and established an isomorphism between this set and that of all the principal derivations on a distributive hyperlattice. [ABSTRACT FROM AUTHOR]

In order to enhance the calculation efficiency of steady-state incompressible fluid flow, based on the existing IDEAL (i.e. the inner doubly iterative efficient algorithm for linked equations) algorithm, a novel segregated pressure-based algorithm (named as IDEALC) has been developed in this paper. The novel algorithm inherits the superiorities of the original IDEAL algorithm and at the same time improves its potential shortcomings. The specific promotions of the IDEALC algorithm consist of three aspects, including the first approximation of the SIMPLE algorithm, the approach to solving the momentum equation and the second approximation of the SIMPLE algorithm. Detailed comparisons between the IDEAL and the IDEALC algorithms are carried out by three numerical experiments on structured collocated grids. The numerical results demonstrate that the IDEALC algorithm can accurately predict the information of the flow field and has substantial advantages over the IDEAL algorithm in terms of the efficiency because of the consistent property of the former. The superiority of the IDEALC algorithm over the IDEAL algorithm is especially remarkable when the time step multiplier gets a moderate value. [ABSTRACT FROM AUTHOR]

Let C n denote the order-preserving and decreasing full transformation semigroup on X n = { 1 , 2 , ... , n } . In this paper, first we describe each principal ideal of C n . Second, we discuss left and right abundance of the principal ideals of C n . Further, necessary and sufficient conditions for the principal ideals in C n to be abundant and regular are given. Finally, we study abundance of the ideals in C n . [ABSTRACT FROM AUTHOR]

The study of symmetry is one of the most important and beautiful themes uniting various areas of contemporary arithmetic. Algebraic structures are useful structures in pure mathematics for learning a geometrical object's symmetries. In this paper, we introduce new concepts in an algebraic structure called BCI-algebra, where we present the concepts of bipolar fuzzy (closed) BCI-positive implicative ideals and bipolar fuzzy (closed) BCI-commutative ideals of BCI-algebras. The relationship between bipolar fuzzy (closed) BCI-positive implicative ideals and bipolar fuzzy ideals is investigated, and various conditions are provided for a bipolar fuzzy ideal to be a bipolar fuzzy BCI-positive implicative ideal. Furthermore, conditions are presented for a bipolar fuzzy (closed) ideal to be a bipolar fuzzy BCI-commutative ideal. [ABSTRACT FROM AUTHOR]

We give a counterexample in this amendment to show that there is an error in consideration of the statement "if f: X → Y and J is an ideal on Y, then f-1(J) = ff-1(J): J ℇ J- is an ideal on X" by Hamlett in his paper "Lindelöf with respect to an ideal" [New Zealand J. Math. 42, 115-120, 2012]. We also modify it here in a new way and henceforth put forward correctly all the results that were based on the said statement derived therein. [ABSTRACT FROM AUTHOR]

To evaluate the goodness-of-fit of a statistical model to given data, calculating a conditional p value by a Markov chain Monte Carlo method is one of the effective approaches. For this purpose, a Markov basis plays an important role because it guarantees the connectivity of the chain, which is needed for unbiasedness of the estimation, and therefore is investigated in various settings such as incomplete tables or subtable sum constraints. In this paper, we consider the two-way change-point model for the ladder determinantal table, which is an extension of these two previous works, i.e., works on incomplete tables by Aoki and Takemura (2005, J. Stat. Comput. Simulat.) and subtable some constraints by Hara, Takemura and Yoshida (2010, J. Pure Appl. Algebra). Our main result is based on the theory of Gröbner basis for the distributive lattice. We give a numerical example for actual data. [ABSTRACT FROM AUTHOR]

We prove that it is relatively consistent with \mathsf {ZFC} that every maximal ideal is Katětov above of all F_\sigma ideals. In particular, we prove that it is consistent that there is no Hausdorff ultrafilter. The main theorem answers questions from Mauro Di Nasso and Marco Forti [Proc. Amer. Math. Soc. 134 (2006), pp. 1809–1818], Jana Flašková [WDS'05 proceedings of contributed papers: part I - mathematics and computer sciences, 2005; Comment. Math. Univ. Carolin. 47 (2006), pp. 617–621; 10th Asian logic conference, World Sci. Publ., Hackensack, NJ, 2010], Osvaldo Guzmán and Michael Hrušák [Topology Appl. 259 (2019), pp. 242–250], and Mauro Di Nasso and Marco Forti [Logic and its applications, Contemp. Math., Amer. Math. Soc., Providence, RI, 2005], and gives a different model for a question from Michael Benedikt [J. Symb. Log. 63 (1998), pp. 638–662], which was originally solved by S. Shelah [Logic colloquium '95 (Haifa), lecture notes logic, Springer, Berlin, 1998]. [ABSTRACT FROM AUTHOR]

Copyright of Arab Journal of Science & Research Publishing is the property of Mussasat Al-Majallah Al-Arabiyah lil-Ulum Wa-Nashr Al-Abhath and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if f (x) R g (x) = 0 for polynomials f (x) = ∑ i = 0 m a i x i , g (x) = ∑ j = 0 m b j x j over any ring R , then for any i , j , there exist positive integers s (i , j) and t (i , j) such that a i 1 R a i 2 R ⋯ a i s (i , j) R b j = 0 and a i R b j 1 R b j 2 R ⋯ R b j t (i , j) = 0 , whenever i 1 , i 2 , ... , i s (i , j) ≤ i and j 1 , j 2 , ... , j t (i , j) ≤ j. Next we prove that if f (x) R g (x) = 0 for power series f (x) = ∑ i = 0 ∞ a i x i , g (x) = ∑ j = 0 ∞ b j x j over any ring R , then for any i , j , there exist positive integers s (i , j) and t (i , j) such that a i s (i , j) R ⋯ R a i 2 R a i 1 R b j 1 R b j 2 R ⋯ R b j t (i , j) = 0 when ∑ p = 1 s (i , j) i p + ∑ q = 1 t (i , j) j q < (s (i , j) + 1) (t (i , j) + 1) (i + 1) (j + 1) and i p ≤ i , j q ≤ j for each p , q. [ABSTRACT FROM AUTHOR]

In this paper, we characterize those rings A and complete Brouwerian residuated lattices L whose residuated lattice F i d (A , L) , of L-fuzzy ideals of A , forms a Boolean algebra. [ABSTRACT FROM AUTHOR]

Copyright of Interstudia is the property of Alma Mater and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let L be an algebra over a field F with the binary operations + and [·, ·]. Then L is called a left Leibniz algebra if it satisfies the left Leibniz identity [[a, b], c] = [a, [b, c]] − [b, [a, c]] for all a, b, c ∈ L. This paper is a brief reviewof some current results,which related to finite- dimensional and infinitedimensional Leibniz algebras. [ABSTRACT FROM AUTHOR]

After the pioneering work of Zadeh[35], a huge number of research papers have been appeared on fuzzy theory and its applications as well as fuzzy analogues of the classical theories. Fuzzy set theory is a powerful hand set for modelling uncertainty and vagueness in various problems arising in field of science and engineering. It has a wide range of applications in various fields: population dynamics[1], chaos control[4], computer programming[5], nonlinear dynamical system[6], etc. Fuzzy topology is one of the most important and useful tools and it proves to be very useful for dealing with such situations where the use of classical theories breaks down. In this paper, we introduce ideal convergence of double sequences in intuitionistic fuzzy sequences defined by compact operator and study the fuzzy topology on the said spaces. [ABSTRACT FROM AUTHOR]

In this paper, we make further investigation on I- convergence of filters and introduce I- closed sets in a topological space. We have used I- closed sets to determine topology on an arbitrary set. [ABSTRACT FROM AUTHOR]

The notions of ideals and filters have studied in many algebraic (crisp) fuzzy structures and used to study their various properties, representations and characterizations. In addition to their theoretical roles, they have used in some areas of applied mathematics. In a recent paper, Arockiarani and Antony Crispin Sweety have generalized and studied these notions with respect to the concept of neutrosophic sets introduced by Smarandache to represent imprecise, incomplete and inconsistent information. In this article, we aim to deepen the study of these important notions on a given lattice in the neutrosophic setting. We show their various properties and characterizations, in particular, we pay attention to their characterizations based on of the lattice min and max operations. In addition, we study the notion of prime single-valued neutrosophic ideal (respectively, filter) as interesting kind and we discuss some its set-operations, complement and associate sets. [ABSTRACT FROM AUTHOR]

Let P be a poset and α : P → P be a function. The aim of this paper is to introduce and study the notion of skew derivations on P. We prove some fundamental properties of posets involving skew derivations. In particular, apart from proving the other results, we prove that if d and g are two skew derivations of P associated with an automorphism α such that d α = α d and g α = α g , then d ≤ g if and only if g d = α d . Also, we prove that F i x α , d (P) ∩ l (α (x)) = l (d (x)) for all x ∈ P. Furthermore, we give some examples to demonstrate that various restrictions imposed in the hypotheses of our results are not superfluous. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to introduce some algebraic properties of finite linear Diophantine fuzzy subsets of group, ring and field. Relatedly, we define the concepts of linear Diophantine fuzzy subgroup and normal subgroup of a group, linear Diophantine fuzzy subring and ideal of a ring, and linear Diophantine fuzzy subfield of a field. We investigate their basic properties, relations and characterizations in detail. Furthermore, we establish the homomorphic images and preimages of the emerged linear Diophantine fuzzy algebraic structures. Finally, we describe linear Diophantine fuzzy code and investigate the relationships between this code and some linear Diophantine fuzzy algebraic structures. [ABSTRACT FROM AUTHOR]

Let H m , n be the mn2-dimensional Radford Hopf algebra over an algebraically closed field of characteristic zero. In this paper, we show that any finite dimensional indecomposable H m , n -module is a cyclic module. According to the structure of any indecomposable module under the adjoint action of H m , n , we prove that the Radford Hopf algebra H m , n is a principal ideal ring. Furthermore, we give explicitly the generators of all 28 ideals of 9-dimensional Radford Hopf algebra H 1 , 3 . [ABSTRACT FROM AUTHOR]

Let (S, ·, ≤) be an ordered semigroup and let A be a nonempty subset of S. The radical of A, denoted √A, is √A = {x ∈ S | xn ∈ A for some positive integer n}. The paper characterizes when the radical √Q is a subsemigroup of S for all quasi-ideals Q of S. [ABSTRACT FROM AUTHOR]

In this paper, we study homomorphic images of interval valued L-fuzzy ideals of a nearring. If f : N1 → N2 is an onto nearring homomorphism and ... is an interval valued L-fuzzy ideal of N2 then we prove that f −1(... ) is an interval valued L-fuzzy ideal of N1 . If ... is an interval valued L-fuzzy ideal of N1 then we show that f (... ) is an interval valued L-fuzzy ideal of N2 whenever ...is invariant under f and interval valued t-norm is idempotent. Finally, we define interval valued L-fuzzy cosets and prove isomorphism theorems. [ABSTRACT FROM AUTHOR]

May soon be invented quantum computer and some known cryptosystems (such as RSA) will be threatened breaking. This paper is aimed at establishing necessary conditions for the maximum possible algebraic generalization of the classical RSA algorithm. We substitute ideals of a Dedekind ring for integers. Ideals in Dedekind rings allow the unique decomposition into a product of maximal ideals, but may not be the principal ideals. Also we define Euler's ϕ-function for ideal of a Dedekind ring and describe some properties of this function. We hope that our proposed method will help to develop algorithms for encryption, which is hard to crack using a quantum computer. [ABSTRACT FROM AUTHOR]

The inclusion ideal graph I n (S) of a semigroup S is an undirected simple graph whose vertices are all the nontrivial left ideals of S and two distinct left ideals I , J are adjacent if and only if either I ⊂ J or J ⊂ I. The purpose of this paper is to study algebraic properties of the semigroup S as well as graph theoretic properties of I n (S). We investigate the connectedness of I n (S) and show that the diameter of I n (S) is at most 3 if it is connected. We also obtain a necessary and sufficient condition of S such that the clique number of I n (S) is the number of minimal left ideals of S. Further, various graph invariants of I n (S) , viz. perfectness, planarity, girth, etc., are discussed. For a completely simple semigroup S , we investigate properties of I n (S) including its independence number and matching number. Finally, we obtain the automorphism group of I n (S). [ABSTRACT FROM AUTHOR]

Copyright of Ideas y Valores is the property of Universidad Nacional de Colombia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The aim of the paper is to introduce a new class of rings — the inner generalized Weyl algebras (IGWA) — and to give simplicity criteria for them. For each IGWA A a derivative series of IGWAs, A → A′→ A″ →⋯ → A(α) →⋯, is attached where α is an arbitrary ordinal. In general, all rings A(α) are distinct. A new construction of rings, the inner (σ,τ,a)-extension of a ring, is introduced (where σ and τ are endomorphisms of a ring D and a ∈ D). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of Ehoops, which are generalizations of hoops. Unlike the hoop, an Ehoop does not necessarily have a top element. The notions of ideals and filters in Ehoops are defined. In Ehoops, both ideals and filters can be used to define the congruences. It is proved that if an Ehoop A satisfies the double negation property, there is a one-to-one correspondence between the set of all ideals of A and the set of all congruences on A. Prime ideal theorem on Ehoops is also given. In addition, we define the notions of implicative filters and positive implicative filters of Ehoops and investigate the quotient algebras induced by (positive) implicative filters. [ABSTRACT FROM AUTHOR]

In random experiments, the fact that the sets of events has a structure of a Boolean algebra, i.e. it follows the rules of classical logic, is the main hypothesis of classical probability theory. Bosbach states have been introduced on commutative and non-commutative algebras of fuzzy logics as a way of probabilistically evaluating the formulas. In this paper, we focus on the relationship between some properties of ideals and Bosbach states in the framework of commutative residuated lattices. In particular, we introduce the concept of co-kernel of a Bosbach state which is an ideal and we establish the relationship between the notion of co-kernel and the kernel. Moreover, we define and characterize maximal ideals and maximal MV-ideals in residuated lattices. [ABSTRACT FROM AUTHOR]

Let T(X) be the full transformation semigroup on the set X . For a fixed nonempty subset Y of X, let PGY (X) = {α ∈ T(X) : α|Y ∈ G(Y )} where G(Y ) is the permutation group on Y . It is known that P GY (X) is a regular subsemigroup of T(X). In this paper, we give a simpler description of Green’s relations and characterize the ideals of P GY (X). Moreover, we prove some isomorphism theorems for PGY (X). For finite sets, we investigate the cardinalities of PGY (X) and of its subsets of idempotents, and we also calculate their ranks. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the concepts of para and quasi topological MV -algebras, which was first introduced by Najafi et al. in 2017, to BL-algebras as para and quasi topological BL-algebras and elaborate these concepts via some examples. We further derive and prove some theorems by employing pre-filters and a fundamental system of neighborhoods. [ABSTRACT FROM AUTHOR]

In this paper, we consider the well‐posedness issue for the density‐dependent incompressible viscoelastic fluids of the Oldroyd model for the ideal case in space dimension greater than 2. We obtain the local well‐posedness of this model under the assumption that the initial density is bounded away from zero in the critical Besov spaces by means of the Littlewood‐Paley theory and Bony's paradifferential calculus. In particular, we obtain a Beale‐Kato‐Majida–type regularity criterion. [ABSTRACT FROM AUTHOR]

Copyright of Karaelmas Science & Engineering Journal / Karaelmas Fen ve Mühendislik Dergisi is the property of Karaelmas Science & Engineering Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we introduce the concepts of I and I-convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of I and I-Cauchy sequences in the gradual normed linear space and investigate the relations between them. [ABSTRACT FROM AUTHOR]

In this paper we study δ -ideals of a pseudocomplemented semilattice. We give some characterizations of δ -ideals. We also prove Stone type separation theorem for δ -ideals of a pseudocomplemented semilattice. We show that the set of δ -ideals of a pseudocomplemented semilattice form a distributive pseudocomplemented lattice. We also prove that the set of principal δ -ideals form a Boolean algebra. [ABSTRACT FROM AUTHOR]