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Licensed Unlicensed Requires Authentication Published by De Gruyter 2023

On modules whose closed M-cyclic submodules are summands

From the book Advances in Pure and Applied Algebra

  • A. J. Gupta and Sanjeev Kumar Maurya

Abstract

A module M whose closed M-cyclic submodules are direct summands is called a CMS module. A CMS module is a nontrivial generalization of a CS module (or an extending module). In this paper, we study more properties of CMS modules and provide a condition under which a CMS module becomes a CS module. Further, we show that the direct sum of two CMS modules is CMS and characterize Noetherian V-rings with the help of CMS modules.

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