罗朗级数环的主拟Baer性  

Principal Quasi-Baerness of Laurent Series Rings

作　　者：刘仲奎[1] 

机构地区：[1]西北师范大学数学系,甘肃兰州730070

出　　处：《数学学报（中文版）》2002年第6期1107-1112,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10171082);NWNU-KJCXGC212资助项目

摘　　要：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.Abstract A ring R is called right principally quasi-Baer (or simply right p.q.Baer) if the right annihilator of every principal right ideal of R is generated by an idempotent. It is shown that for a ring R with SJ(R)(?)C(R), R[[x, x-1]] 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). It is also shown that a ring R is right p.q.Baer if and only if R[x, x-1] is right p.q.Baer.

关 键 词：主拟Baer性 右p.q.Baer环 罗朗级数环 罗朗多项式环 

分 类 号：O153.3[理学—数学]