On Strongly Ɣ-Clean Rings

Abstract

For any element z of a ring R is said to be Ɣ-clean if z=a+e, where a is γ-regular and e is an idempotent, further if ae=ea , the element z is called strongly Ɣ-clean. If all the elements of a ring R is Ɣ-clean (resp. strongly Ɣ-clean), then R is called an Ɣ-clean (strongly Ɣ-clean). In this paper, some examples, and properties of Ɣ-clean and strongly Ɣ-clean are introduced and invest gules the behavior of these properties and discuss some relations between Ɣ-clean (resp., strongly Ɣ-clean) rings and other rings.