A new class of dual notions: $S$-co-$r$-submodules and $S$-co-$n$-submodules based on multiplicatively closed subsets

Articles in Press

Document Type : Research Paper

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Department of Mathematics, Payame Noor University, P.O.BOX 19395-3697, Tehran, Iran

Abstract

Let $R$ be a commutative ring, $M$ be an $R$-module and $S\subseteq R$ be a multiplicatively closed subset of $R$. The purpose of this paper is to introduce and investigate the concepts of $S$-co-$r$-submodules and $S$-co-$n$-submodules by using the notion of a multiplicatively closed subset of $R$. A non-zero submodule $N$ of $M$ with $Rad(Ann(M))\cap S=\emptyset$ is called an $S$-co-$n$-submodule, if there exists $s\in S$ such that whenever $aN\subseteq K$ and $sa\not \in Rad(Ann(M))$ for some $a\in R$ and a submodule $K$ of $M$, then $sN\subseteq K$. Many properties and examples are given of such submodules. Also, we state the correspondence between $S$-co-$r$-submodules and $S$-co-$n$-submodules.
 

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References

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Algebraic Structures and Their Applications

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Available Online from 12 November 2025

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