On Strongly F – Regular Modules and Strongly Pure Intersection Property

Abstract

A submoduleA of amodule M is said to be strongly pure , if for each finite subset {a i } in A , (equivalently, for each a A) there exists ahomomorphism f : M A such that f(a i ) = a i , i(f(a)=a). A module M is said to be strongly F-regular if each submodule of M is strongly pure . The main purpose of this paper is to develop the properties of strongly F-regular modules and study modules with the property that the intersection of any two strongly pure submodules is strongly pure .