Ore扩张的PP性和PS性

Ore extensions of PP and PS rings.

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.