On S-primary submodules

TL;DR

This paper explores properties of S-primary submodules in modules over commutative rings, expanding the understanding of their structure and relation to primary and S-prime submodules.

Contribution

It introduces and investigates S-primary submodules, showing they properly contain primary and S-prime submodules, thus broadening the class of submodules studied.

Findings

S-primary submodules form a larger class than primary submodules.

S-primary submodules properly contain primary and S-prime submodules.

The paper establishes properties and relationships among these classes.

Abstract

Let $R$ be a commutative ring with identity, $S$ a multiplicatively closed subset of $R$, and $M$ be an $R$-module. In this paper, we study and investigate some properties of $S$-primary submodules of $M$. Among the other results, it is shown that this class of modules contains the family of primary (resp. $S$-prime) submodules properly.