On Cofinitely Weak Rad-Supplemented Modules

Abstract

In this paper, necessary and sufficient conditions for a quotient module are found to be a cofinitely weak Rad-supplemented module under which circumstances. Nevertheless, some relations are investigated between cofinitely Rad-supplemented modules and cofinitely weak Rad-supplemented modules. Lastly, we show that an arbitrary ring R is a left Noetherian V - ring if and only if every weak Rad-supplemented R - module is injective.