A Note on Regular Qclean Rings

Ashrafi and Nasibi introduced the notion of r-clean rings, where each element of ring is the sum of an idempotent and von Neumann regular element (an element x is an element of R is a von-neumann regular if there exists h is an element of R such that xhx = x). Motivated by this structure, we introduce here the notion of regular qclean ring by replacing idempotent element by q-potent element in.r -clean ring. In this article, we focus to study the fundamental properties of regular qclean rings and also discussed some properties of matrix rings in context of regular qclean rings. Apart from this, we find some conditions on ring so that the ring of ideal extension is regular qclean.