Special regular clean rings

In this paper we introduce the concepts of special regular clean elements and regular clean decomposition in a ring R. These concepts lead us to the notion of special regular clean ring. We prove that for a special regular clean element a=e+r \in R and unit u\in R then au is a special regular clean if u is an inner inverse of e. We establish that an abelian ring R is a special regular clean ring if and only if the twisted power series ring R[[x,\sigma]] is a special regular clean ring. We also study various characterizations of special clean and special regular clean rings.

Special regular clean rings Keywords:

r-clean ring , Special clean ring , Special rclean ring , Twisted power series ring