Direct Summands of ⊕-Supplemented Modules

Abstract

A module M is called ⊕-supplemented if every submodule of M has a supplement that is a direct summand of M. It is shown that if M is a ⊕-supplemented module and r(M) is a coclosed submodule of M for a left preradical r, then r(M) is a direct summand of M, and both r(M) and M/r(M) are ⊕-supplemented.

On a variation of ⊕-supplemented modules

“…Over a Dedekind domain, it is proven in [3, Proposition A.7 and Proposition A.8] that every supplemented module is ⊕-supplemented. For the basic properties, characterizations and some generalizations of ⊕-supplemented modules, we recommend the book [3] and these papers [6][7][8][9][10][11].…”