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On weakly S-prime submodules

Authors :
Khashan, Hani A.
Celikel, Ece Yetkin
Publication Year :
2021

Abstract

Let $R$ be a commutative ring with a non-zero identity, $S$ be a multiplicatively closed subset of $R$ and $M$ be a unital $R$-module. In this paper, we define a submodule $N$ of $M$ with $(N:_{R}M)\cap S=\phi$ to be weakly $S$-prime if there exists $s\in S$ such that whenever $a\in R$ and $m\in M$ with $0\neq am\in N$, then either $sa\in(N:_{R}M)$ or $sm\in N$. Many properties, examples and characterizations of weakly $S$-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly $S$-prime.

Subjects

Subjects :
Mathematics - Commutative Algebra

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2110.14639
Document Type :
Working Paper