Generalized \(\oplus\)-supplemented modules
Abstract
Let \(R\) be a ring and \(M\) be a left \(R\)-module. \(M\) is called generalized \(\oplus\)- supplemented if every submodule of \(M\) has a generalized supplement that is a direct summand of \(M\). In this paper we give various properties of such modules. We show that any finite direct sum of generalized \(\oplus\)-supplemented modules is generalized \(\oplus\)-supplemented. If \(M\) is a generalized \(\oplus\)-supplemented module with \((D3)\), then every direct summand of \(M\) is generalized \(\oplus\)-supplemented. We also give some properties of generalized cover.
Keywords
generalized cover, generalized supplemented module, \(\oplus\)-supplemented module, generalized \(\oplus\)-supplemented module
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