Some results on countably $\sum$−uniform - extending modules

Abstract

A module $M$ is called a uniform extending if every uniform submodule of $M$ is essential in a direct summand of $M$. A module $M$ is called a countably $\sum$− uniform extending if $M^{(NƯ$) is uniform extending. In this paper, we discuss the question of when a countably $\sum$− uniform extending module is $\sum$− quasi - injective? We also characterize of rings by the class of countably $\sum$− uniform extending modules.