| 任艳丽,王尧.分次环的分次Excellent扩张[J].数学研究及应用,2007,27(3):586~590 |
| 分次环的分次Excellent扩张 |
| Graded Excellent Extensions of Graded Rings |
| 投稿时间：2005-06-07 修订日期：2006-07-02 |
| DOI：10.3770/j.issn:1000-341X.2007.03.018 |
| 中文关键词: 分次Excellent扩张 分次右$V$-环 分次$PS$-环 分次Von Neumann正则环. |
| 英文关键词:graded excellent extension graded right $V$-ring graded $PS$-ring graded Von Neumann regular ring. |
| 基金项目:国家自然科学基金 (10471055); 辽宁省教育厅科学研究基金(05L014). |
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| 中文摘要: |
| 本文引进了分次环的分次Excellent扩张概念.设$S=\bigoplus_{g\in G}S_g$是$R=\bigoplus_{g\in G}R_g$的分次Excellent扩张,证明了$S$是分次右$V$-环当且仅当$R$是分次右$V$-环,$S$是分次$PS$-环当且仅当$R$是分次$PS$-环,$S$是分次Von Neumann正则环当且仅当$R$是分次Von Neumann正则环. |
| 英文摘要: |
| The concept of graded excellent extension of graded rings is introduced. Let $S=\bigoplus_{g\in G}S_g$ be a graded excellent extension of $R=\bigoplus_{g\in G}R_g$. We prove that $S$ is a graded right $V$-ring if and only if $R$ is a graded right $V$-ring, $S$ is graded $PS$-ring if and only if $R$ is a graded $PS$-ring, and $S$ is a Von Neumann regular ring if and only if $R$ is a graded Von Neumann regular ring. |
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