Fully $S$-coidempotent modules

TL;DR

This paper introduces and explores the properties of fully S-coidempotent modules, generalizing existing concepts of coidempotent modules within the context of commutative rings and multiplicatively closed subsets.

Contribution

It defines the new classes of S-coidempotent submodules and fully S-coidempotent modules, extending the theory of coidempotent modules in module theory.

Findings

Basic properties of S-coidempotent submodules established

Characterizations of fully S-coidempotent modules provided

Generalizations of coidempotent modules discussed

Abstract

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.