| 彭宅铭,谷勤勤,赵良.幺半群上的斜强可逆环[J].数学研究及应用,2016,36(1):43~50 |
| 幺半群上的斜强可逆环 |
| On Skew Strongly Reversible Rings Relative to a Monoid |
| 投稿时间：2014-12-30 修订日期：2015-03-20 |
| DOI：10.3770/j.issn:2095-2651.2016.01.006 |
| 中文关键词: 可逆环 斜强$M$-可逆环 斜半群环 |
| 英文关键词:reversible rings skew strongly $M$-reversible rings skew monoid rings |
| 基金项目:安徽省高校省级优秀青年人才基金重点项目基金(Grant No.2012SQRL039ZD),安徽工业大学研究生创新基金(Grant No.2014163). |
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| 中文摘要: |
| 对于幺半群$M$, 本文介绍了强$M$-可逆环的推广斜强$M$-可逆环及其性质. 如果$G$是有限阿贝尔群, 则$G$是无挠的当且仅当存在环$R$, 当$|R|\geq 2$ 时$R$ 是斜强$M$- 可逆环. 如果$R$是有古典右商环$Q$的右Ore环, 则$R$是斜强$M$-可逆当且仅当$Q$是斜强$M$-可逆. |
| 英文摘要: |
| For a monoid $M$, we introduce the concept of skew strongly $M$-reversible rings which is a generalization of strongly $M$-reversible rings, and investigate their properties. It is shown that if $G$ is a finitely generated Abelian group, then $G$ is torsion-free if and only if there exists a ring $R$ with $|R| \geq 2$ such that $R$ is skew strongly $G$-reversible. Moreover, we prove that if $R$ is a right Ore ring with classical right quotient ring $Q$, then $R$ is skew strongly $M$-reversible if and only if $Q$ is skew strongly $M$-reversible. |
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