Skew Hurwitz series over quasi Baer and PS-rings

Abstract

In this paper, we consider some properties of rings which are shared by the ring R and the ring T = (HR, σ ) of skew Hurwitz series. In particular we show that:
1) If R is a ring with char(R) = 0 and σ is an R -automorphism such that σ (e) = e and the left annihilator of every left ideal is σ -invariant, then the following are equivalent:
i) T is a quasi Baer ring.
ii) R is a quasi Baer ring.
2) If R is a right PS-ring with char(R) = 0, then T is a right PS-ring.