MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Y. Tolooei

Volume 8, Issue 1 , September 2020, Pages 1-5
Abstract
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)\leq 1$, multiplication modules ...  Read More

CLASSICAL 2-ABSORBING SECONDARY SUBMODULES

Volume 8, Issue 1 , September 2020, Pages 7-15
Abstract
‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎‎identity‎. ‎We ...  Read More

ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS

M. R. Ahmadi Zand; S. Rostami

Volume 8, Issue 1 , September 2020, Pages 17-26
Abstract
Abstract. A topological group H is called ω -narrow if for everyneighbourhood V of it’s identity element there exists a countableset A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ Gsuch that xe(x) = e(x)x ...  Read More

A NEW CHARACTERIZATION OF ABSOLUTELY PO-PURE AND ABSOLUTELY PURE S-POSETS

R. Khosravi; M. Roueentan

Volume 8, Issue 1 , September 2020, Pages 27-37
Abstract
In this paper, we investigate po-purity using ﬁnitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly ﬁnitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented ...  Read More

ADMITTING CENTER MAPS ON MULTIPLICATIVE METRIC SPACE

M. H. LABBAF Ghasemi Zavareh; N. Eftekhari; A. Bayati Eshkaftaki

Volume 8, Issue 1 , September 2020, Pages 39-51
Abstract
‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps ...  Read More

PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE

H. Bijari; K. Khashyarmanesh; H. Fazaeli Moghim

Volume 8, Issue 1 , September 2020, Pages 53-68
Abstract
‎‎Let $R$ be a commutative ring with identity and let $M$ be an $R$-module‎. ‎We define the primary spectrum of $M$‎, ‎denoted by $\mathcal{PS}(M)$‎, ‎to be the set of all primary submodules $Q$ of $M$ such that $(\operatorname{rad}Q:M)=\sqrt{(Q:M)}$‎. ‎In this ...  Read More

$\varphi$-CONNES MODULE AMENABILITY OF DUAL BANACH ALGEBRAS

A. Ghaffari; S. Javadi Syahkale; E. Tamimi

Volume 8, Issue 1 , September 2020, Pages 69-82
Abstract
In this paper we define $\varphi$-Connes module amenability ofa dual Banach algebra $\mathcal{A}$ where $\varphi$ is a bounded $w_{k^*}$-modulehomomorphism from $\mathcal{A}$ to $\mathcal{A}$. We are mainlyconcerned with the study of $\varphi$-module normalvirtual diagonals. We show that if $S$ is a ...  Read More

THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G

Gh. A. Nasiriboroujeni; M. Mirzavaziri; A. Erfanian

Volume 8, Issue 1 , September 2020, Pages 83-93
Abstract
To a simple graph $G=(V,E)$, we correspond a simple graph $G_{\triangle,\square}$ whose vertex set is $\{\{x,y\}: x,y\in V\}$ and two vertices $\{x,y\},\{z,w\}\in G_{\triangle,\square}$ are adjacent if and only if $\{x,z\},\{x,w\},\{y,z\},\{y,w\}\in V\cup E$. The graph $G_{\triangle,\square}$ is called ...  Read More

ANNIHILATOR OF LOCAL COHOMOLOGY MODULES UNDER THE RING EXTENSION R⊂R[X]

M. Seidali Samani; K. Bahmanpour

Volume 8, Issue 1 , September 2020, Pages 95-102
Abstract
Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of localcohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp.R⊂R[[X]]). By using this extension we will present some of the faithfulness ...  Read More

A NEW CHARACTERIZATION OF SIMPLE GROUP G 2 (q) WHERE q ⩽ 11

Volume 8, Issue 1 , September 2020, Pages 103-111
Abstract
In this paper, we prove that every finite group $G$ with the same order and largest element order as $G_{2}(q)$, where $q\leq 11$ is necessarily isomorphic to the group $G_{2}(q)$.  Read More

A GENERALIZATION OF PRIME HYPERIDEALS

M. Anbarloei

Volume 8, Issue 1 , September 2020, Pages 113-127
Abstract
‎‎Let $R$ be a multiplicative hyperring‎. In this paper‎, ‎we introduce and study the concept of n-absorbing hyperideal which is a generalization‎‎of prime hyperideal‎. ‎A proper hyperideal $I$ of $R$ is called an $n$-absorbing hyperideal of ‎$‎R‎$‎ ...  Read More