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Faranak Farshadifar

Publications and source records attributed to Faranak Farshadifar.

13 recordsLinked to original sources
arXiv2026

The $i$-extended ideal-based cozero-divisor graph of a commutative ring

Let R be a commutative ring with identity and let J be an ideal of R. In this paper, we introduce and investigate the notion of the i-extended ideal-based cozero-divisor graph of R. This graph, denoted by $\overline{\Gamma''}_{Ji}(R)$, is a simple graph of R whose vertex set is ${x \in R \ J : xR + J \not= R}$. Two distinct vertices $x$ and $y$ are adjacent if and only if $x^m \not \in y^nR+J$ and $y^n \not \in x^mR+J$ for some positive integers m and n with $n\leq i$ and $m\leq i$.

math.AC↗
arXiv2025

nil-$M$-Noetherian and nil-$M$-Artinian modules

Let R be a commutative ring with identity and M be an R- module. The aim of this paper is to introduce and investigate the notions of nil-M-Noetherian and nil-M-Artinian modules as generalizations of Noetherian and Artinian modules. Also, in this regard we introduce nil versions of some algebraic concepts.

math.AC↗
arXiv2025

Second semimodules over commutative semirings

Let R be a semiring. We say that a non-zero subsemimodule S of an R-semimodule M is second if for each a \in R, we have aS = S or aS = 0. The aim of this paper is to study the notion of second subsemimodules of semimodules over commutative semirings.

math.AC↗
arXiv2025

Some graphs related to submodules of a module

Let R be a commutative ring with identity and M be an R-module. In this paper, we introduce and investigate the second submodule intersection graph SSI(M) of M with vertices are nonzero proper submodules of M and two distinct vertices N and K are adjacent if and only if is a second submodule of M. Also, we introduce and consider the prime submodule sum graph PSS(M) of M with vertices are non-zero proper submodules of M and two distinct vertices N and K are adjacent if and only if N + K is a prime submodule of M.

math.AC↗
arXiv2025

Nil-prime ideals of a commutative ring

Let R be a commutative ring with identity and N(R) be the set of all nilpotent elements of R. The aim of this paper is to introduce and study the notion of nil-prime ideals as a generalization of prime ideals. We say that a proper ideal P of R is a nil-prime ideal if there exists x \in N(R) and whenever ab \in P, then a \in P or b \in P or a+x \in P or b+x \in P for each a,b \in R. Also, we introduce nil versions of some algebraic concepts in ring theory such as nil-maximal ideal, nil-minimal ideal, nil-principal ideal and investigate some nil-version of a well-known results about them.

math.AC↗
arXiv2024

Survey on second submodules of modules over commutative rings

Let R be a commutative ring with identity. The concept of second submodule of an R-module (as a dual notion of prime submodules) was introduced and studied by S.Yassemi in 2001. This notion has obtained a great attention by many authors and now there is a considerable amount of research concerning this class of modules. The main purpose of this paper is to collect these results and provide a useful source for those who are interested in research in this field.

math.AC↗
arXiv2022

The duals of annihilator conditions for modules

Let R be a commutative ring with identity and let M be an R-module. The purpose of this paper is to introduce and investigate the submodules of an R-module M which satisfy the dual of Property A, the dual of strong Property A, and the dual of proper strong Property A. Moreover, a submodule N of M which satisfy Property SJ (N) and Property IM J (N) will be introduced and investigated.

math.AC↗
arXiv2020

$S$-secondary submodules of a module

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. The aim of this paper is to introduce the notion of S-secondary submodules of M as a generalization of secondary submodules of M and investigate some properties of this class of submodules.

math.AC↗
arXiv2020

Fully $S$-idempotent modules

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The aim of this paper is to introduce the notion of fully S-idempotent modules as a generalization of fully idempotent modules and investigate some properties of this class of modules.

math.AC↗
arXiv2020

$S$-2-absorbing submodules and $S$-2-absorbing second submodules

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. In this paper, we introduce the notion of S-2-absorbing second submodules of M as a generalization of S-second submodules and strongly 2-absorbing second submodules of M. We investigate some properties of this class of submodules. Also, we obtain some results concerning S-2-absorbing submodules of M.

math.AC↗
arXiv2019

2-irreducible and strongly 2-irreducible submodules of a module

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 generalization of irreducible (resp., strongly irreducible) submodules of M and investigated some properties of these classes of modules.

math.AC↗