宋军全.迭代的斜多项式环的Baer和拟-Baer性[J].数学研究及应用,2006,26(1):103~106
迭代的斜多项式环的Baer和拟-Baer性
Baer and Quasi-Baer Rings of Iterated Skew Polynomial Rings
投稿时间:2003-08-20  
DOI:10.3770/j.issn:1000-341X.2006.01.017
中文关键词:  迭代的斜多项式环  (拟)Baer环  $\alpha$-rigid.
英文关键词:iterated skew ploynomial ring  quasi-Baer ring  $\alpha$-rigid.
基金项目:
作者单位
宋军全 浙江工业大学应用数学系, 浙江 杭州 310014 
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中文摘要:
      本文主要讨论了环$R$和迭代的斜多项式环$T(u)$的零化子之间的关系,从而得出在一定条件下,$R$是Baer环当且仅当$T(u)$是Baer环.而对于拟-Baer性,只要$R$是拟Baer环就行了,作为推论我们证明了sl(2)的包络代数和量子包络代数都是拟Baer环.
英文摘要:
      We study the relations between the set of annihilators in $R$ and the set of annihilators in iterated skew polynomial ring $T(u)$, and then we show that $R$ is Baer ring if and only if $T(u)$ is Baer ring under certain conditions. In addition we prove that if $R$ is quasi-Baer ring so is $T(u)$, and as a concequence we show that the (quantum) enveloping algebra of sl(2) is quasi-Baer ring.
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