关于Baer PP和PS环的一些性质(英)

Some Properties on Baer PP and PS Rings

中文关键词:  Bare环  PP环  PS环  Strong-Armendariz环  Ore-扩张.

英文关键词:Baer ring  PP ring  PS ring  Strong-Armendariz ring  Ore extension.

中文摘要:

      在此文中,我们对 Strong-Armendariz 环和 Baer PP 及PS 环Ore-扩张 $R[x,x^{-1};\alpha]$的一些性质进行了讨论研究,并得到了一些结果. 主要证明了$R$是Baer(PP)环当且仅当 $R[[x]]$ 是Baer(PP)环及 $R$ 是 $\alpha$-rigid环时, $R$是 Baer(PP,PS)环当且仅当 $R[[x]]$ 是Baer(PP,PS)环.

英文摘要:

      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.