Strongly Uniform Extending Modules

Abstract

In this paper, we introduced and studied the concept of strongly uniform extending modules, an R-module M is called strongly uniform extending (or M has (1-SC1) condition) if every uniform submodule of M is essential in a stable (fully invariant) direct summand of M. As a proper stronger than uniform extending modules and as a generalization of strongly extending modules and give some properties of such modules in analogy with properties for strongly extending modules. We have the following implications:Strongly extending modules ⇒ strongly uniform extending modules ⇒ Uniform extending modules.