Generalized ⊕-Supplemented Modules

Abstract

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