Clean rings of skew Hurwitz series

Abstract

In this paper we study the transfer of some algebraic properties from the ring R to the ring of skew Hurwitz series T = (H R, σ ) where σ is an automorphism of R and vice versa. We show that T = (H R, σ ) is a clean (strongly clean) ring if and only if R is clean (strongly clean). Different properties of skew Hurwitz series are studied such as simplicity, primeness and semiprime.