On modules whose closed M-cyclic submodules are summands

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 U-rings with the help of CMS modules. © 2023 Walter de Gruyter GmbH, Berlin/Bostonl. All rights reserved.