| 幺半群上的斜强可逆环 |
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| 引用本文： | 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 |
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| 作者姓名： | 彭宅铭 谷勤勤 赵良 |
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| 作者单位： | 安徽工业大学数理科学与工程学院, 安徽 马鞍山 243032;安徽工业大学数理科学与工程学院, 安徽 马鞍山 243032;安徽工业大学数理科学与工程学院, 安徽 马鞍山 243032 |
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| 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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| 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| ≥ 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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| 关 键 词： | 可逆环 斜强$M$-可逆环 斜半群环 |
| 收稿时间： | 2014-12-30 |
| 修稿时间： | 2015-03-20 |
On Skew Strongly Reversible Rings Relative to a Monoid |
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| Zhaiming PENG,Qingqin GU and Liang ZHAO. On Skew Strongly Reversible Rings Relative to a Monoid[J]. Journal of Mathematical Research with Applications, 2016, 36(1): 43-50 |
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| Authors: | Zhaiming PENG Qingqin GU Liang ZHAO |
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| Affiliation: | School of Mathematics & Physics, Anhui University of Technology, Anhui 243032, P. R. China;School of Mathematics & Physics, Anhui University of Technology, Anhui 243032, P. R. China;School of Mathematics & Physics, Anhui University of Technology, Anhui 243032, P. R. China |
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| Abstract: | 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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| Keywords: | reversible rings skew strongly $M$-reversible rings skew monoid rings |
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