Modules for which every non-cosingular submodule is a summand

Document Type: Research Paper

Authors

Department of Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Mazandaran‎, ‎Babolsar‎, ‎Iran.

Abstract

‎A module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some general properties of NS-modules‎. ‎Several‎ ‎examples are provided to separate different concepts‎. ‎It is shown that every non-cosingular‎ ‎NS-module is a direct sum of indecomposable modules‎. ‎We‎ ‎also discuss on finite direct sums of NS-modules.

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