On idempotent elements

الملخص EN

In this paper we study idempotent elements, we give some new properties of idempotent elements and provide some exam we also study central idempotent elements and orthogonal idempotent elements and give some new properties of such idempotent.

Finally we study special ring which satisfies the property for all x in R and n is a positive integer, we represent such ring in termes of idempotent and nilpotent elements.