Retractable Modules Relative To A Submodule And Some Generalizations

Abstract

A new generalizations of retractable modules relative to a submodule are introduced where a module ℳ is called retractable module relative to a submodule N of M if for all non-zero submodule K of ℳ such that contains N, there exists a non-zero homomorphism f∈Hom(ℳ, K). Some basic properties are studied and many relationships between these classes and other related concepts are presented and studied.