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.
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