斜幂级数环的主拟Baer性(英文)

Principal Quasi-Baerness of Skew Power Series Rings

中文关键词:  弱刚性自同态  主拟Baer环  斜幂级数环

英文关键词:weakly rigid endomorphism  p.q.Baer ring  skew power series ring.

中文摘要:

      设R是环,并且R的左半中心幂等元都是中心幂等元, α是R的一个弱刚性自同态. 本文证明了斜幂级数环R[[x,α]]是右主拟Baer环当且仅当R是右主拟Baer环,并且R的任意可数幂等元集在I(R)中有广义交,其中I(R)是R的幂等元集.

英文摘要:

      Let R be a ring such that all left semicentral idempotents axe central and α a weakly rigid endomorphism of R. It is shown that the skew power series ring R[[x; α]] is right p.q.Baer if and only if R is right p.q.Baer and any countable family of idempotents in R has a generalized join in I(R), where I(R) is the set of all idempotents of R.