Strongly Uniform Extending Modules
Keywords:strongly uniform extending, strongly uniform continuous, strongly uniform quasi-continuous
AbstractIn 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.
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