Ore扩张的PP性和PS性  

Ore extensions of PP and PS rings.

作　　者：宋军全[1] 

机构地区：[1]浙江大学数学系

出　　处：《浙江大学学报（理学版）》2004年第1期10-13,共4页Journal of Zhejiang University（Science Edition）

摘　　要：CHANYong-hong等证明了:假如R是α-rigid环,那么R是PP环当且仅当R[x;α,δ]是PP环.作者将这个结论推广到了斜幂级数环R[[x;α]]上.证明了如果R是α-rigid环,那么R[[x;α]]是PP环当且仅当R是PP环且R中可数个幂等元在B(R)中有最小上界.同时讨论了Ore扩张和斜幂级数的广义PP性、弱PP性、p.q-Baer性以及PS性.It was proved by CHAN Yong-hong et al. that if R is α-rigid then R is PP ring if and only if R[x;α,δ] is PP ring. It was proved that if R is α-rigid, then R[[x;α]] is PP ring if and only if R is PP ring and any countable family of idempotents in R has a join in B(R). In addition, it was studied that the Ore extensions and skew power series of generalized PP rings, weak PP rings, p.q-Baer rings and PS rings.

关 键 词：ORE扩张 斜幂级数环 PP环 P.q-Baer环 PS环 

分 类 号：O153.3[理学—数学]