Some Properties on Baer PP and PS Rings

Abstract:

      This paper gives some results on Strong-Armendariz rings and the Ore-extensions $R[x,x^{-1}; \alpha]$ of Bare, PP and PS rings. And the main two results are: (1) $R$ is a Bear (PP) ring if and only if $R[[x]]$ is a Baer (PP) ring; (2) If $R$ is an $\alpha$-rigid ring, then $R$ is a Baer (PP, PS) ring if and only if $R[x,x^{-1}; \alpha]$ is a Baer (PP, PS) ring.