Fully $S$-idempotent modules

TL;DR

This paper introduces fully S-idempotent modules, a generalization of fully idempotent modules, and explores their properties within the context of modules over commutative rings with identity.

Contribution

It defines the concept of fully S-idempotent modules and investigates their fundamental properties, extending the theory of idempotent modules.

Findings

Introduction of fully S-idempotent modules

Characterization of properties of these modules

Extension of existing module theory

Abstract

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The aim of this paper is to introduce the notion of fully S-idempotent modules as a generalization of fully idempotent modules and investigate some properties of this class of modules.