On CLS-modules and the S-closure of a submodule

Document Type : Research Paper


Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran


A module $M$ is called a $CLS$-module if every ${S}$-closed submodule of $M$  is a direct summand of $M$ [9]. We give a characterization for $CLS$-modules and obtain a sufficient condition for $CLS$-submodules of a $CLS$-module. Also, we characterize the splitting property in terms of  $UT$-modules and the $S$-closure of submodules.


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Volume 14, Issue 7
July 2023
Pages 327-330
  • Receive Date: 18 August 2022
  • Revise Date: 28 October 2022
  • Accept Date: 03 November 2022