@article { author = {Farshadifar, Faranak}, title = {Fully $S$-idempotent modules}, journal = {Khayyam Journal of Mathematics}, volume = {9}, number = {1}, pages = {153-161}, year = {2023}, publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)}, issn = {2423-4788}, eissn = {2423-4788}, doi = {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 = {Idempotent submodule‎,‎Fully idempotent module‎,‎Multiplicatively closed subset‎,‎$S$-Idempotent submodule‎,‎Fully $S$-idempotent module}, url = {https://www.kjm-math.org/article_164491.html}, eprint = {https://www.kjm-math.org/article_164491_aa3a414cd8221acda43f8775017db403.pdf} }