tg-Radical Supplemented Modules

Abstract

In this work, we define tg-radical supplemented modules and cofinitely tg-radical supplemented modules. We investigate some properties of these modules. In addition, we present examples separating the tg-radical supplemented modules, g-supplemented modules, and ⊕-g-Rad-supplemented modules and also show the equality of these modules for projective and finitely generated modules. We give a characterization of cofinitely tg-radical supplemented modules. Furthermore, for any ring R, we show that any finite direct sum of tg-radical supplemented R-modules is tg-radical supplemented and that any direct sum of cofinitely tg-radical supplemented R-modules is a cofinitely tg-radical supplemented module.