Study on nil and nilpotent rings and modules

Abstract

A submodule of a right -module is called a nilpotent submodule of if is a right nilpotent ideal of and is a nil submodule of if is a right nil ideal of . By definition, a nilpotent submodule is a nil submodule. It is seen that is a fully invariant nilpotent submodule of if and only if is a two-sided nilpotent ideal of . Modifying the structure of nil and nilpotent right ideals over associative arbitrary rings, present study develops some properties of nil and nilpotent submodules over associative endomorphism rings. Some characterizations of nil and nilpotent submodules over associative endomorphism rings are also investigated in the present study.