On f-clean rings and f-clean elements

Abstract

An associative ring R with identity is called f -clean ring if every element in R is the sum of an idempotent and a full element. In this paper, various basic properties of f -clean rings and f -clean elements are proved. Also, we give some new charaterizations of f -clean rings. In addition, we prove that the ring of skew Hurwitz series T = (HR, σ) where σ is an automorphism of R is f -clean if and only if R is f -clean.