王占平.对称环的扩张[J].数学研究及应用,2007,27(2):229~235
对称环的扩张
Extensions of Symmetric Rings
投稿时间:2005-03-24  修订日期:2006-03-07
DOI:10.3770/j.issn:1000-341X.2007.02.002
中文关键词:  对称环  平凡扩张  多项式环  古典右商环.
英文关键词:symmetric ring  trivial extension  polynomial ring  classical right quotient ring.
基金项目:
作者单位
王占平 西北师范大学数学系, 甘肃 兰州 730070 
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中文摘要:
      本文首先考虑了对称环的性质和基本的扩张.其次讨论了几种多项式环的对称性,且证明了:如果$R$是约化环,则$R[x]/(x^{n})$是对称环,其中$(x^{n})$是由$x^{n}$生成的理想, $n$是一个正整数.最后证明了:对一个右Ore环$R$, $R$是对称环当且仅当$R$的古典右商环$Q$是对称环.
英文摘要:
      We first consider properties and basic extensions of symmetric rings. We next argue about the symmetry of some kinds of polynomial rings, and show that if $R$ is a reduced ring then $R[x]/(x^{n})$ is a symmetric ring, where $(x^{n})$ is the ideal generated by $x^{n}$ and $n$ is a positive integer. Consequently, we prove that for a right Ore ring $R$ with $Q$ its classical right quotient ring, $R$ is symmetric if and only if $Q$ is symmetric.
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