arXiv subjects
Publications and source records attributed to F. Farshadifar.
Let R be a commutative ring with identity and I be an ideal of R. The cozero-divisor graph with respect to I, denoted by $\Gamma''_I(R)$, is the graph of R with vertices {x \in R -I :xR +I \not=R} and two distinct vertices $x$ and $y$ are adjacent if and only if $x \not \in yR+I$ and $y \not \in xR+I$.In this paper, we obtained some results on $\Gamma''_I(R)$.
Let R be a commutative ring with identity and M be an R-module. A proper ideal I of R is said to be a $z^\circ$-ideal if for each $a \in I$ the intersection of all minimal prime ideals containing a is contained in I. The purpose of this paper is to introduce the notion of $z^\circ$-submodules of M as an extension of $z^\circ$-ideals of R. Moreover, we investigate some properties of this class of submodules when M is a reduced multiplication R-module.
Let R be a commutative ring with identity, and let I be an ideal of R. The zero-divisor graph of R with respect to I, denoted by $\Gamma_I(R)$, is the graph whose vertices are the set $\{x \in R \setminus I | xy \in I$ for some $y \in R \setminus I\}$, where distinct vertices x and y are adjacent if and only if $xy \in I$. The cozero-divisor graph with respect to I, denoted by $\Gamma''_I(R)$, is the graph of $R$ with vertices $\{x \in R \setminus I | xR + I \neq R\}$, and two distinct vertices x and y are adjacent if and only if $x \notin yR + I$ and $y \notin xR + I$. In this paper, we introduce and investigate an undirected graph $Q\Gamma''_I(R)$ of R with vertices $\{x \in R \setminus \sqrt{I} | xR + I \neq R$ and $xR + \sqrt{I} = xR + I\}$ and two distinct vertices x and y are adjacent if and only if $x \notin yR + I$ and $y \notin xR + I$.
Let R be a commutative ring with identity. In this paper, we introduce and investigate the second ideal intersection graph SII(R) of R with vertices are non-zero proper ideals of R and two distinct vertices I and J are adjacent if and only if $I \cap J$ is a second ideal of R.
Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduced the dual notion of z-submodules of M and some of extensions. Moreover, we investigate some properties of these classes of modules when M is a coreduced comultiplication R-module.
This paper deals with some results concerning finitely generated coreduced comultiplication modules over a commutative ring.
Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to defined the notion of quasi $z^\circ$-submodules of M as an extension of $z^\circ$-ideals of R and obtained some related results when M is a reduced multiplication R-module.
Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduce and investigate the dual notions of r-submodules, n-submodules, and J-submodules of M.
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-coidempotent R-modules as generalizations of coidempotent submodules and fully coidempotent R-modules. We explore some basic properties of these classes of R-modules.
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 submodules of M as a generalization of strongly 2-absorbing second and ψ-second submodules of M.
Let R be a commutative ring with identity and M be an R-module. The main purpose of this paper is to introduce and study the notion of $ψ$-second submodules of an R-module M.
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 strongly prime ideals. Furthermore, we investigate some basic properties of these classes of ideals.
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-absorbing (resp. strongly 2-absorbing) second submodules and investigate some basic properties of these classes of modules.
Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we introduce the cozero-divisor graph $\acuteΓ_I(R)$ of $R$ and obtain some related results.
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 modules and investigate some basic properties of these classes of modules.
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.
Let $R$ be a commutative ring and $M$ an $R$-module. Let $Spec^s(M)$ be the the collection of all second submodules of $M$. In this article, we consider a new topology on $Spec^s(M)$, called the second classical Zariski topology, and investigate the interplay between the module theoretic properties of $M$ and the topological properties of $Spec^s(M)$. Moreover, we study $Spec^s(M)$ from point of view of spectral space.