Graph explorer

r-clean rings

An element of a ring R is called clean if it is the sum of an idempotent and a unit. A ring R is called clean if each of its element is clean. An element r \in R called regular if r = ryr for some y \in R. The ring R is regular if each of its element is regular. In this paper we define a ring is r-clean if each of its elements is the sum of a regular and an idempotent element. We give some relations between r-clean and clean rings. Finally we investigate some properties of r-clean rings.