# Fully $S$-idempotent modules

Document Type : Original Article

Author

Department of Mathematics, Farhangian University, Tehran, Iran

10.22034/kjm.2022.362523.2664

Abstract

‎Let $R$ be a commutative ring with identity‎, ‎$S$ be a multiplicatively closed subset of $R$‎, ‎and $M$ be an $R$-module‎. A submodule $N$ of $M$ is said to be \emph{idempotent} if $N=(N:_RM)^2M$‎. ‎Also‎, ‎$M$ is said to be \emph{fully idempotent} if every submodule of $M$ is idempotent‎. 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.

Keywords