Results 1 to 10 of about 57 (51)

The intersection graph of annihilator submodules of a module [PDF]

Opuscula Mathematica, 2019
Let \(R\) be a commutative ring and \(M\) be a Noetherian \(R\)-module. The intersection graph of annihilator submodules of \(M\), denoted by \(GA(M)\) is an undirected simple graph whose vertices are the classes of elements of \(Z_R(M)\setminus \text ...
S.B. Pejman, Sh. Payrovi, S. Babaei
doaj   +2 more sources

Annihilator Essential Submodules

Journal of Physics: Conference Series, 2021
Abstract Through this paper R represent a commutative ring with identity and all R-modules are unitary left R-modules. In this work we consider a generalization of the class of essential submodules namely annihilator essential submodules.
Sahira M Yaseen
exaly   +2 more sources

Annihilator large-superfluous submodules

Journal of Physics: Conference Series, 2021
Abstract In this paper, we investigate certain class of submodules which contains that of superfluous submodules. A submodule W of an R-module M is annihilator large-superfluous, if ℓS(V) ≠ 0 implies that W + V ≠ M where V is a large in M and S = End R(M). Several properties and characterizations of such submodules are consider. For α∈ S,
exaly   +2 more sources

THE ANNIHILATOR GRAPH FOR MODULED OVER COMMUTATIVE RINGS [PDF]

Journal of Algebraic Systems, 2021
‎Let $R$ be a commutative ring and $M$ be an $R$-module‎. ‎The‎ ‎annihilator graph of $M$‎, ‎denoted by $AG(M)$ is a simple undirected‎ ‎graph associated to $M$ whose the set of vertices is‎ ‎$Z_R(M) \setminus {\rm Ann}_R(M)$ and two distinct vertices $x$
Katayoun Nozari, Sh. Payrovi
doaj   +1 more source

On the strongly annihilating-submodule graph of a module

Hacettepe Journal of Mathematics and Statistics, 2022
In this paper we continue to study the strongly annihilating-submodule graph. In addition to providing the more properties of this graph, we compare extensively the properties of this graph with the annihilating-submodule graph.
Reza BEYRANVAND, Ahadollah FARZI-SAFARABADI   +1 more
openaire   +4 more sources

ON COMULTIPLICATION AND R-MULTIPLICATION MODULES [PDF]

Journal of Algebraic Systems, 2014
We state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings.
Ashkan Nikseresht, Habib Sharif
doaj   +1 more source

R-annihilator-Coessential and R-annihilator-Coclosed Submodules

Iraqi Journal of Science, 2020
Let be a unitary left R-module on associative ring with identity. A submodule of is called -annihilator small if , where is a submodule of , implies that ann( )=0, where ann( ) indicates annihilator of in . In this paper, we introduce the concepts of -annihilator-coessential and - annihilator - coclosed submodules.
Omar K. Ibrahim, Alaa A. Elewi
openaire   +2 more sources

The annihilating-submodule graph of modules over commutative rings II [PDF]

Arabian Journal of Mathematics, 2016
Let M be a module over a commutative ring R. In this paper, we continue our study of annihilating-submodule graph AG(M) which was introduced in (The Zariski topology-graph of modules over commutative rings, Comm. Algebra., 42 (2014), 3283{3296). AG(M) is a (undirected) graph in which a nonzero submodule N of M is a vertex if and only if there exists a ...
Ansari-Toroghy, Habibollah, Habibi, Shokoufeh   +1 more
openaire   +4 more sources

DOMINATION NUMBER IN THE ANNIHILATING-SUBMODULE GRAPH OF MODULES OVER COMMUTATIVE RINGS

International Electronic Journal of Algebra, 2021
Let $M$ be a module over a commutative ring $R$. The annihilating-submodule graph of $M$, denoted by $AG(M)$, is a simple undirected graph in which a non-zero submodule $N$ of $M$ is a vertex if and only if there exists a non-zero proper submodule $K$ of $M$ such that $NK=(0)$, where $NK$, the product of $N$ and $K$, is ...
ANSARI-TOROGHY, Habibollah, HABIBI, Shokoufeh   +1 more
openaire   +4 more sources

A NEW CLASS OF SMALL SUBMODULES [PDF]

Journal of Algebraic Systems
Let $R$ be a commutative ring with identity $1\neq 0$ and $M$ a nonzero unital $R$-module. In this paper, we introduce a new notion of submodules in $M$, namely $T$-semi-annihilator small submodules of $M$ with respect to an arbitrary submodule $T$ of $M$
Farkhondeh Farzalipour, Saeed Rajaee, Marzieh Poyan   +2 more
doaj   +1 more source