16 citations · 25 across the 14 of their papers we have counts for
16 papers
On S-primary submodules
H. Ansari-Toroghy, S. S. Pourmortazavi
Let be a commutative ring with identity, a multiplicatively closed subset of , and be an -module. In this paper, we study and investigate some properties of -p…
Fully -coidempotent modules
F. Farshadifar, H. Ansari-Toroghy
Let R be be a commutative ring with identity and S be a multiplicatively closed subset of R. In this article we introduce the concepts of S-coidempotent submodules and fully S-coid…
Strongly --absorbing second submodules
H. Ansari-Toroghy, F. Farshadifar, S. Maleki-Roudposhti
Let R be a commutative ring with identity and M be an R-module. The main purpose of this paper is to introduce and investigate the notion of strongly ψ-2-absorbing second submodule…
The Zariski topology-graph of modules over commutative rings II
Habibollah Ansari-Toroghy, Shokoufeh Habibi
Let be a module over a commutative ring . In this paper, we continue our study about the Zariski topology-graph which was introduced in (The Zariski topology-graph…
Domination number in the annihilating-submodule graph of modules over commutative rings
Habibollah Ansari-Toroghy, Shokoufeh Habibi
Let be a module over a commutative ring . The annihilating-submodule graph of , denoted by , is a simple graph in which a non-zero submodule of is a vertex…
Some generalizations of strongly prime ideals
H. Ansari-Toroghy, F. Farshadifar, S. Maleki-Roudposhti
In this paper, we introduce the concepts of strongly 2-absorbing primary ideals (resp., submodules) and strongly 2-absorbing ideals (resp., submodules) as generalizations of strong…
2-irreducible and strongly 2-irreducible submodules of a module
Faranak Farshadifar, Habibollah Ansari-Toroghy
Let R be a commutative ring with identity and M be an R-module. In this paper, we will introduce the concept of 2-irreducible (resp., strongly 2- irreducible) submodules of M as a…
An ideal-based cozero-divisor graph of a commutative ring
H. Ansari-Toroghy, F. Farshadifar, F. Mahboobi-Abkenar
Let be a commutative ring and let be an ideal of . In this paper, we introduce the cozero-divisor graph of and obtain some related results.
2-absorbing and strongly 2-absorbing secondary submodules of modules
H. Ansari-Toroghy, F. Farshadifar
In this paper, we will introduce the concept of 2-absorbing (resp. strongly 2-absorbing) secondary submodules of modules over a commutative ring as a generalization of secondary mo…
Classical and strongly classical 2-absorbing second submodules
H. Ansari-Toroghy, F. Farshadifar
In this paper, we will introduce the concept of classical (resp. strongly classical) 2-absorbing second submodules of modules over a commutative ring as a generalization of 2-absor…
Some generalizations of second submodules
H. Ansari-Toroghy, F. Farshadifar
In this paper, we will introduce two generalizations of second submodules of a module over a commutative ring and explore some basic properties of these classes of modules.
The large sum graph related to comultiplication modules
H. Ansari-Toroghy, F. Mahboobi-Abkenar
Let R be a commutative ring and M be an R-module. We define the large sum graph, denoted by \acute{G}(M), as a graph with the vertex set of non-large submodules of M and two distin…
The annihilating-submodule graph of modules over commutative rings II
Habibollah Ansari-Toroghy, Shokoufeh Habibi
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 modul…
The annihilating-submodule graph of modules over commutative rings
Habibollah Ansari-Toroghy, Shokoufeh Habibi
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 modul…
The Zariski topology-graph on the maximal spectrum of modules over commutative rings
Habibollah Ansari-Toroghy, Shokoufeh Habibi
Let M be a module over a commutative ring and let Spec(M) (resp. Max(M)) be the collection of all prime (resp. maximal) submodules of M. We topologize Spec(M) with Zariski topology…
On the second spectrum of a module (II)
H. Ansari-Toroghy, S. Keyvani, F. Farshadifar
Let be a commutative ring and an -module. Let be the the collection of all second submodules of . In this article, we consider a new topology on $Spec^s(M…