Modules Whose Submodules Are Strongly Stable Relative To An Ideal

Abstract

In this work, the notion of fully strongly stable modules relative to an ideal has been introduced and studied which is stronger than those of fully stable modules and fully stable modules relative to an ideal. Several properties and characterizations have been given. Endomorphism ring of this class of modules has been studied and criteria given, that an endomorphism ring is fully strongly stable relative to an ideal by using categorical concepts.characterization of submodules have been given in terms of some residual condition, and the property that each submodule is idempotent relative to an ideal.