Sh. Payrovi
Imam Khomeini International University
[ 1 ] - On the 2-absorbing Submodules
Let $R$ be a commutative ring and $M$ be an $R$-module. In this paper, we investigate some properties of 2-absorbing submodules of $M$. It is shown that $N$ is a 2-absorbing submodule of $M$ if and only if whenever $IJLsubseteq N$ for some ideals $I,J$ of R and a submodule $L$ of $M$, then $ILsubseteq N$ or $JLsubseteq N$ or $IJsubseteq N:_RM$. Also, if $N$ is a 2-absorbing submodule of ...
[ 2 ] - On the Associated Primes of the generalized $d$-Local Cohomology Modules
The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary generalized local cohomology modules. Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$ are finitely generated $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...
[ 3 ] - A Submodule-Based Zero Divisors Graph for Modules
Let $R$ be commutative ring with identity and $M$ be an $R$-module. The zero divisor graph of $M$ is denoted $Gamma{(M)}$. In this study, we are going to generalize the zero divisor graph $Gamma(M)$ to submodule-based zero divisor graph $Gamma(M, N)$ by replacing elements whose product is zero with elements whose product is in some submodules $N$ of $M$. The main objective of this pa...
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