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Modules for which every non-cosingular submodule is a summand. (English) Zbl 1403.16003

Summary: 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.

MSC:

16D10 General module theory in associative algebras
16D80 Other classes of modules and ideals in associative algebras
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