Minimal prime ideals of skew Hurwitz series ring

Abstract

Let R be a ring with an endomorphism α. In this paper we obtain necessary and sufficient conditions on R and α such that the skew Hurwitz series ring (HR, α) is a 2-primal ring. In particular, it is proved that, under suitable conditions, (HR,α) is 2-primal if and only if for every minimal prime ideal P^∗ in (HR, α) there exists a minimal prime ideal P of R such that P is completely prime and P^∗=(HP,α) if and only if P((HR,α))=(H(nil(R)),α) if and only if R is 2-primal and nil((HR,α))=(H(nil(R)),α) if and only if every minimal α-prime ideal of R is completely prime.