فهرست نشریات علمی دسترسی آزاد ایران

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.