Abstract
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.
Highlights
In this paper we study idempotent elements, we give some new properties of idempotent elements and provide some exam we study central idempotent elements and orthogonal idempotent elements and give some new properties of such idempotent
Throughout this paper R denotes an associative rings with identity
Recall that: (1)A ring R is said to be reduced if R contains no non zero nilpotent elements.(2) For any element a of a ring R we define the right annihilator of a in R by, r(a) = x R : ax = 0, and likewise the left annihilator of a.in R
Summary
In this paper we study idempotent elements, we give some new properties of idempotent elements and provide some exam we study central idempotent elements and orthogonal idempotent elements and give some new properties of such idempotent. في هذا البحث درسنا العناصر المتحايدة و أعطينا خواص جديدة لها . و أعطينا تمثيلا لهذه الحلقة بدلالة العناصر المتحايدة و المعدومة القوى،
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