Principal Quasi-Baerness of Rings of Generalized Power Series

Let R be a ring such that all left semicentral idempotents are central and （S, ≤） a strictly totally ordered monoid satisfying that 0 ≤s for all s ∈S. It is shown that [[R^S≤]], the ring of generalized power series with coefficients in R and exponents in S, is right p.q.Baer if and only if R is right p.q.Baer and any S-indexed subset of I（R） has a generalized join in I（R）, where I（R） is the set of all idempotents of R.

Principal Quasi-Baerness of Rings of Skew Generalized Power Series

Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,（R） has a generalized join in S,（R）. Several known results follow as consequences of our results.

斜多项式环R[x,σ]是p.q-Baer环的充分条件

设σ是环R的一个自同构 .证明了如果R是σ 右p q Baer环 ,并且Sσl 的任意元e满足 :对任意的r∈R及任意非负整数i,erσ-i(e) =rσ-i(e) ;对任意的r∈R ,若re=0 ,则rσ(e) =0 ,那么环R的斜多项式扩张R[x ,σ]是右p q

环的(主)拟-Baer性在Morita Context环上的推广

通过反例得出Baer环不具有Movita不变性的结论。在此基础上,探讨了含有2个模零同态的MoritaContext环构成Baer环、拟-Baer环和右主拟-Baer环的条件,得到含有2个零模的Morita Context环构成Baer环、拟-Baer环和右主拟-Baer环的充要条件,并将所得结果推广到三阶Morita Context环。

Principal Quasi-Baerness of Skew Power Series Rings

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.

罗朗级数环的主拟Baer性

称环 R为右主拟 Baer环（简称为右p·q.Baer环）,如果 R的任意主右理想的右零化子可由幂等元生成.本文证明了,若环 R满足条件Sl（R）（?）C（R）,则罗朗级数环R[[x,x-1]]是右p.q.Baer环当且仅当R是右p.q.Baer环且R的任意可数多个幂等元在I（R）中有广义join.同时还证明了,R是右p.q.Baer环当且仅当R[x,x-1]是右P.q.Baer环.