Modules for which every non-cosingular submodule is a summand
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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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Journal title
volume 43 issue 3
pages 911- 922
publication date 2017-06-01
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