Shahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901STRUCTURE OF ZERO-DIVISOR GRAPHS ASSOCIATED TO RING OF INTEGER MODULO n114266210.22044/jas.2022.11719.1599ENShariefuddinPirzadaDepartment of Mathematics, University of Kashmir, Srinagar, India.AaqibAltafDepartment of Mathematics, University of Kashmir, Srinagar, India.SaleemKhanDepartment of Mathematics, University of Kashmir, Srinagar, India.Journal Article20220303For a commutative ring $R$ with identity $1\neq 0$, let $Z^{*}(R)=Z(R)\setminus \lbrace 0\rbrace$ be the set of non-zero zero-divisors of $R$, where $Z(R)$ is the set of all zero-divisors of $R$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is a simple graph whose vertex set is $Z^{*}(R)=Z(R)\setminus \{0\}$ and two vertices of $ Z^*(R)$ are adjacent if and only if their product is $ 0 $. In this article, we find the structure of the zero-divisor graphs $ \Gamma(\mathbb{Z}_{n}) $, for $n=p^{N_1}q^{N_2}r$, where $2<p<q<r$ are primes and $N_1$ and $N_2$ are positive integers.https://jas.shahroodut.ac.ir/article_2662_5c12fb2660f3006615d619d7ebbbd933.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901THE STRUCTURE OF MODULE LIE DERIVATIONS ON TRIANGULAR BANACH ALGEBRAS1526266310.22044/jas.2022.10734.1530ENMohammad RezaMiriDepartment of Mathematics, University of Birjand, P.O. Box 9717434765, Birjand,
Iran.EbrahimNasrabadiDepartment of Mathematics, University of Birjand, P.O. Box 9717434765, Birjand,
Iran.Ali RezaGhorchizadehDepartment of Mathematics, University of Birjand, P.O. Box 9717434765, Birjand,
Iran.Journal Article20210420In this paper, we introduce the concept of module Lie derivations on Banach algebras and study module Lie derivations on unital triangular Banach algebras $ \mathcal{T}=\begin{bmatrix}A & M\\ &B\end{bmatrix}$ to its dual. Indeed, we prove that every module (linear) Lie derivation\linebreak $ \delta: \mathcal{T} \to \mathcal{T}^{\ast}$ can be decomposed as $ \delta = d + \tau $, where $ d: \mathcal{T} \to \mathcal{T}^{\ast} $ is a module (linear) derivation and $ \tau: \mathcal{T} \to Z_{\mathcal{T}}(\mathcal{T}^{\ast}) $ is a module (linear) map vanishing at commutators if and only if this happens for the corner algebras $A$ and $B$.https://jas.shahroodut.ac.ir/article_2663_7713a9edadd19c2ba563752dfb94d31f.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901TWO PROPERTIES OF COUSIN FUNCTORS2736266410.22044/jas.2022.11632.1592ENAlirezaVahidiDepartment of Mathematics, Payame Noor University, Tehran, Iran.FaisalHassaniDepartment of Mathematics, Payame Noor University, Tehran, Iran.MaryamSenshenasDepartment of Mathematics, Payame Noor University, Tehran, Iran.Journal Article20220205Let $R$ be a commutative Noetherian ring with non-zero identity and $\mathcal{F}$ a filtration of $\operatorname{Spec}(R)$. We show that the Cousin functor with respect to $\mathcal{F}$, $C_R(\mathcal{F},-):\mathcal{C}_{\mathcal{F}}(R)\longrightarrow\operatorname{Comp}(R)$, where $\mathcal{C}_{\mathcal{F}}(R)$ is the category of $R$-modules which are admitted by $\mathcal{F}$ and $\operatorname{Comp}(R)$ is the category of complexes of $R$-modules, commutes with the formation of direct limits and is right exact. We observe that an $R$-module $X$ is balanced big Cohen-Macaulay if $(R,\mathfrak{m})$ is a local ring, $\mathfrak{m}X\neq X$, and every finitely generated submodule of $X$ is a big Cohen-Macaulay $R$-module with respect to some system of parameters for $R$.https://jas.shahroodut.ac.ir/article_2664_303abbdd182a064a3e42f9c51c9ce28a.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901ACENTRALIZERS OF GROUPS OF ORDER p33743266510.22044/jas.2022.11069.1547ENZahraMozafarDepartment of Mathematical Sciences, Isfahan University of Technology, P. O. Box
84156-83111, Isfahan, Iran.BijanTaeriDepartment of Mathematical Sciences, Isfahan University of Technology, P. O. Box
84156-83111, Isfahan, Iran.Journal Article20210806Suppose that $G$ is a finite group. The acentralizer $C_G(\alpha)$ of an automorphism $\alpha$ of $G$,<br />is defined as the subgroup of fixed points of $\alpha$, that is $C_G(\alpha)= \{g \in G \mid \alpha(g)=g\}$.<br />In this paper we determine the acentralizers of groups of order $p^3$, where $p$ is a prime number.https://jas.shahroodut.ac.ir/article_2665_eddc75f64ccd1400acac3b4a8c2129f2.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901INTRINSIC IDEALS OF DISTRIBUTIVE LATTICES4564266610.22044/jas.2022.11321.1565ENSAMBASIVA RAOMUKKAMALADepartment of Mathematics, MVGR College of Engineering, P.O. Box 535004,
Vizianagaram, Andhra Pradesh, India.Journal Article20211021The concepts of intrinsic ideals and inlets are introduced in a distributive lattice. Intrinsic ideals are also characterized with the help of inlets. Certain equivalent conditions are given for an ideal of a distributive lattice to become intrinsic. Some equivalent conditions are derived for the quotient lattice, with respect to a congruence, to become a Boolean algebra. Some topological properties of the prime spectrum of intrinsic ideals of distributive lattice are derived.https://jas.shahroodut.ac.ir/article_2666_8ea67e64d0577e5e08c0780e193e15d0.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901ON THE STRONG DOMINATING SETS OF GRAPHS6576266710.22044/jas.2022.11646.1595ENHassanZaherifarDepartment of Mathematical Sciences, Yazd University, P.O. Box 89195-741, Yazd,
Iran.SaeidAlikhaniDepartment of Mathematical Sciences, Yazd University, P.O. Box 89195-741, Yazd,
Iran.NimaGhanbariDepartment of Informatics, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway.Journal Article20220208Let $G=(V(G),E(G))$ be a simple graph. A set $D\subseteq V(G)$ is a strong dominating set of $G$, if for every vertex $x\in V(G)\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x)\leq deg(y)$. The strong domination number $\gamma_{st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we calculate $\gamma_{st}(G)$ for specific graphs and study the number of strong dominating sets of some graphs.https://jas.shahroodut.ac.ir/article_2667_0b43106dc9e6de4c7ea2480bc3c3007b.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901CHARACTERIZATION OF JORDAN $\{g, h\}$-DERIVATIONS OVER MATRIX ALGEBRAS7795266810.22044/jas.2022.11250.1562ENArindamGhoshDepartment of Mathematics, Government Polytechnic Kishanganj, Thakurganj,
P.O. Box 855116, Kishanganj, India.OmPrakashDepartment of Mathematics, Indian Institute of Technology Patna, P.O. Box 801106,
Patna, India.Journal Article20210927In this article, we characterize $\{g, h\}$-derivation on the upper triangular matrix algebra $\mathcal{T}_n(C)$ and prove that every Jordan $\{g, h\}$-derivation over $\mathcal{T}_n(C)$ is a $\{g, h\}$-derivation under a certain condition, where $C$ is a $2$-torsion free commutative ring with unity $1\neq 0$. Also, we study $\{g, h\}$-derivation and Jordan $\{g, h\}$-derivation over full matrix algebra $\mathcal{M}_n(C)$.https://jas.shahroodut.ac.ir/article_2668_a94d482c950b83c4b684d332282e90cd.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901SOME RESULTS ON THE ARTINIAN COFINITE MODULES97103266910.22044/jas.2022.11608.1588ENGholamrezaPirmohammadiPayame Noor University, P.O. Box 19395-3697, Tehran, Iran.Journal Article20220127Let $I$ be an ideal of a commutative Noetherian ring $R$ and $M$ be a non-zero Artinian $R$-module with support contained in $V(I)$. In this paper it is shown that $M$ is $I$-cofinite if and only if $Rad(I\widehat{R}^J+Ann_{\widehat{R}^J}M)=J\widehat{R}^J$, where $J:=\cap_{m\in Supp M}m$ and $\widehat{R}^J$ denotes the $J$-adic comletion of $R$.https://jas.shahroodut.ac.ir/article_2669_4a9ed13776418a8cc0a74cd7acf108c8.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901(ANTI) FUZZY IDEALS OF SHEFFER STROKE BCK-ALGEBRAS105135267010.22044/jas.2022.11512.1582ENTahsinOnerDepartment of Mathematics, Ege University, Bornova, Izmir, Turkey.TKalkanDepartment of Mathematics, Ege University, Bornova, Izmir, Turkey.ArshamBorumand SaeidDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid
Bahonar University of Kerman, Kerman, Iran.Journal Article20211224The aim of this study is to introduce (anti) fuzzy ideals of a Sheffer stroke BCK-algebra. After describing an anti fuzzy subalgebra and an anti fuzzy (sub-implicative) ideal of a Sheffer stroke BCK-algebra, the relationships of these structures are demonstrated. Also, a t-level cut and a complement of a fuzzy subset are defined and some properties are investigated. An implicative Sheffer stroke BCK-algebra is defined and it is proved that a fuzzy subset of an implicative Sheffer stroke BCK-algebra is an anti fuzzy ideal if and only if it is an anti fuzzy sub-implicative ideal of this algebraic structure. A fuzzy congruence and a fuzzy quotient set of a Sheffer stroke BCK-algebra are studied in details and it is shown that there is a bijection between the set of fuzzy ideals and the set of fuzzy congruences on this algebraic structure. Finally, Cartesian product of fuzzy subsets of a Sheffer stroke BCK-algebra is determined and it is expressed that the Cartesian product of two anti fuzzy ideals of this algebraic structure is anti fuzzy ideal.https://jas.shahroodut.ac.ir/article_2670_53a9cdb49aea8e7c6e3fc127fa3522c6.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901LOCATION OF SOLID BURST WITHIN TWO ADJACENT SUB-BLOCKS137147267110.22044/jas.2022.11136.1552ENPankaj KumarDasDepartment of Mathematical Sciences, Tezpur University, Napaam, P.O. Box 784028,
Sonitpur, Assam, India.Journal Article20210824The paper studies the existence of linear codes that locate solid burst errors, which may be confined to one sub-block or spread over two adjacent sub-blocks. An example of such a code is also given. Comparisons on the number of parity check digits required for such linear codes with solid burst detecting and correcting codes are also provided.https://jas.shahroodut.ac.ir/article_2671_cee666c88f2c501ceb6596c2e04d891e.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901Varieties Of Permutative Semigroups Closed Under Dominions149172267210.22044/jas.2022.12018.1617ENHumairaMaqboolDepartment of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, P.O. Box 192122, Pulwama, India.Mohammad YounusBhatDepartment of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, P.O. Box 192122, Pulwama, India.Journal Article20220620In this paper, we partially generalize a result of Isbell from the class of commu- tative semigroups to some generalized class of commutative semigroups by showing that dominion of such semigroups belongs to the same class by using Isbell’s zigzag theorem. we found some permutative semigroups for which dominion satisfies the identity of subsemigroup of a semigroup S.https://jas.shahroodut.ac.ir/article_2672_ce1ea0de819a1f6b35331b0c6682ec89.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901ON THE FINITENESS OF FORMAL LOCAL COHOMOLOGY MODULES173187267310.22044/jas.2022.11072.1549ENShahramRezaeiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.MahbobehGasemi-KalemasihiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.Journal Article20210807Let a be an ideal of local ring (R;m) and M a nitely generated R-module. In<br />this paper, we prove some results concerning niteness and minimaxness of formal local cohomology<br />modules. In particular, we investigate some properties of top formal local cohomology<br />FdimM=aM<br />a (M) and we determine CosR(FdimM=aM<br />a (M)), AnnR(FdimM=aM<br />a (M)) and<br />AttR(FdimM=aM<br />a (M)).https://jas.shahroodut.ac.ir/article_2673_997180ed18b5a93afe97c72b4b8019fc.pdf