Weak nil clean ideals

Abstract

As a generalization of a nil clean ideal, we define a weak nil clean ideal of a ring. An ideal I of a ring R is said to be weak nil clean ideal if for any $$x\in I$$, either $$x=e+n$$ or $$x=-e+n$$, where n is a nilpotent element and e is an idempotent element of R. Some interesting properties of weak nil clean ideal and its relation with weak nil clean ring have been discussed.