Idempotent Elements and Annihilator Relative to Right Ideal

Abstract

In this paper we study the notion of idempotent elements relative to right ideal, we give other characterization of this elements. Also, we present several examples of idempotent elements relative to right ideal in matrices ring and ring integer modulo .

In addition to that, new results obtained include necessary and sufficient conditions for a some ring to be has idempotent elements in term of matrices ring. Where we obtain the relationship between idempotent elements in some ring and idempotent elements relative to right ideal in matrices ring over this ring.

Finally, we introduced the concept of annihilator of element relative to right ideal as generalization of annihilator of element in some ring. Where we obtain several equivalently conditions of this concept. 

In addition to that, we characterization of this concept in term matrices ring. Where we proved that if is a ring and . Then  if and only if there exists  such that for

,  .