Algebraic Structures and their Applications

Let $R$ be a commutative Noetherian ring with non-zero identity, $mathfrak{a}$ an ideal of $R$, $X$ an arbitrary $R$--module, $mathcal{F}$ a filtration of $operatorname{Spec}(R)$ which admits $X$, and $s, s', t, t'$ non-negative integers such that $s+ t= s'+ t'$. In this paper, we study the membership of $R$--modules $operatorname{H}^{s}_mathfrak{a}(operatorname{H}^{t- 1}(operatorname{C}_R(mathcal{F}, X)))$ and $operatorname{H}^{s'- 1}(operatorname{H}^{t'}_mathfrak{a}(operatorname{C}_R(mathcal{F}, X)))$ in Serre subcategories of the category of $R$--modules and find some sufficient conditions which ensure the existence of an isomorphism between them, where $operatorname{C}_R(mathcal{F},X)$ is the Cousin complex for $X$ with respect to $mathcal{F}$. As applications, we give some new facts and represent some older facts about the local cohomology modules and the Cousin complexes.

Alireza Vahidi

Faisal Hassani

Maryam Senshenas

Algebraic structures and their applications

Local cohomology modules and Cousin complexes

局部上同调模与Cousin复形

Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.

Zahra Heidarian

The existence totally reflexive covers

完全自反覆盖的存在性

Let $G$ be a finite group. The graph $D(G)$ is a divisibility graph of $G$. Its vertex set is the non-central conjugacy class sizes of $G$ and there is an edge between vertices $a$ and $b$ if and only if $a|b$ or $b|a$. In this paper, we investigate the structure of the divisibility graph $D(G)$ for a non-solvable group with $sigma^{ast}(G)=2$, a finite simple group $G$ that satisfies the one-prime power hypothesis, a group of type($A$),($B$) or ($C$) and certain metacyclic $p-$groups and a minimal non-metacyclic $p-$group where $p$ is a prime number. We will show that the divisibility graph $D(G)$ for all of them has no triangles.

Danial Khoshnevis

Zohreh Mostaghim

Some finite groups with divisibility graph containing no triangles

一些有限群的整除图不含三角形

In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.

Moniri Hamzekolaee

Ali Reza

H$^*$-condition on the set of submodules of a module

模的子模集上的H$^*$条件

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we will introduce the notions of 2-absorbing $I$-prime and 2-absorbing $I$-second submodules of an $R$-module $M$ as a generalization of 2-absorbing and strongly 2-absorbing second submodules of $M$ and explore some basic properties of these classes of modules.

Faranak Farshadifar

2-absorbing $I$-prime and 2-absorbing $I$-second submodules

2-吸收$I$-素和2-吸收$I$-第二子模

One of the main goals of science and engineering is to avail human beings cull the maximum propitious decisions. To make these decisions, we need to ken human being's predictions, feasible outcomes of various decisions, and since information is never absolutely precise and accurate, we need to withal information about the degree of certainty. All these types of information will lead to partial orders. A partially ordered set (or poset) theory deals with partial orders and plays a major role in real life. It has wide range of applications in various disciplines such as computer science, engineering, medical field, science, modeling spatial relationship in geographic information systems (GIS), physics and so on. In this paper, we mainly focus on weakly primary semi-ideal of a poset. We introduce the concepts of weakly primary semi-ideal and weakly $Q$-primary semi-ideal for some prime $Q$ of a poset $P$ and characterize weakly primary semi-ideals of $P$ in terms of prime and primary semi-ideals of $P.$ We provide a counter-example for the existence of weakly primary semi-ideal of $P$ which is not a primary semi-ideal of $P.$ We found an equivalent assertion of primary (respy., weakly primary) semi-ideal $r(K)$ for a semi-ideal $K$ of $P.$ Moreover, we introduce the notion of direct product of weakly primary semi-ideal of $P$ and describe its characteristics.

K. Porselvi

B. Elavarasan

Weakly primary semi-ideals in posets

偏序集中的弱主半理想

The notion of $mathcal{K}$-extending modules was defined recently as a proper generalization of both extending modules and Rickart modules. Let $M$ be a right $R$-module and let $S=End_R(M)$. We recall that $M$ is a $mathcal{K}$-extending module if for every element $phiin S$, $Kerphi$ is essential in a direct summand of $M$. Since a direct sum of $mathcal{K}$-extending modules is not a $mathcal{K}$-extending module in general, an open question is to find necessary and sufficient conditions for such a direct sum to be $mathcal{K}$-extending. In this paper, we give an answer to this question. We show that if $M_i$ is $M_j$-injective for all $i, jin I ={1, 2, dots, n}$, then $bigoplus_{i=1}^n M_i$ is a $mathcal{K}$-extending module if and only if $M_i$ is $M_j$-$mathcal{K}$-extending for all $i, j in I$. Other results on $mathcal{K}$-extending modules and some of their applications are also included.

Tayyebeh Amouzegar

An approach to extending modules via homomorphisms

通过同态扩展模的方法

A finite group $G$ is called textit{$(l,m, n)$-generated}, if it is a quotient group of the triangle group $T(l,m, n) = left .$ In 29, Moori posed the question of finding all the $(p,q,r)$ triples, where $p, q$ and $r$ are prime numbers, such that a non-abelian finite simple group $G$ is a $(p,q,r)$-generated. In this paper we establish all the $(p,q,r)$-generations of the symplectic group $Sp(6,2).$ GAP 20 and the Atlas of finite group representations 33 are used in our computations.

Ayoub Basheer

Malebogo John Motalane

Thekiso Trevor Seretlo

The $(p,q,r)$-generations of the symplectic group $Sp(6,2)$

辛群 $Sp(6,2)$ 的 $(p,q,r)$-生成

For a group $G$, $pi_e(G)$ and $s_m(G)$ are denoted the set of orders of elements and the number of elements of order $m$ in $G$, respectively. Let ${rm nse}(G)={s_m(G) | min pi_e(G)}$. An arbitrary finite group $M$ is NSE characterization if, for every group $G$, the equality ${rm nse}(G)={rm nse}(M)$ implies that $Gcong M$. In this paper, we are going to show that the non-Abelian finite simple groups $A_9$, $A_{10}$, $A_{12}$, $U_4(3)$, $U_5(2)$, $U_6(2)$, $S_6(2)$, $O_8^+(2)$ and $HS$ are characterizable by NSE.

Sakineh Rahbariyan

Azizollah Azad

On the NSE characterization of certain finite simple groups

关于某些有限单群的NSE特征

In this paper, we introduce a notion of ultra central approximate identity for Banach algebras which is a generalization of the bounded approximate identity and the central approximate identity. Using this concept we study pseudo-contractibility of some matrix algebras among $ell^1$-Munn algebras. As an application, for the Brandt semigroup $S=M^{0}(G,I)$ over a non-empty set $I$, we show that $ell^{1}(S)$ has an ultra central approximate identity if and only if $I$ is finite. Also we show that the notion of pseudo-contractibility and contractibility are the same on $ell^{1}(S)^{**}$, where $S$ is the Brandt semigroup.

Publication Information	Publisher: Yazd University，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2019，Proportion of original research papers: ，Self Citation Rate:， Gold OA Rate:

Algebraic Structures and their Applications

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