Strongly Nil* Clean Ideals

Abstract

An element  is known a strongly nil* clean element if a=e1 - e1e2 + n , where e1,e2  are idempotents and n is nilpotent, that commute with one another. An ideal I of a ring R is called a strongly nil* clean ideal if each element of I is strongly nil* clean element. We investigate some of its fundamental features, as well as its relationship to the nil clean ideal.

Keywords

• nilpotent element
• jacobson radical
• strongly nil* clean ideal
• idempotent element