| 弱McCoy环的扩张 |
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| 引用本文： | 王尧,任艳丽,李晓伟. 弱McCoy环的扩张[J]. 浙江大学学报(理学版), 2014, 41(4): 376-380. DOI: 10.3785/j.issn.1008-9497.2014.04.003 |
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| 作者姓名： | 王尧 任艳丽 李晓伟 |
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| 作者单位： | 南京信息工程大学数理学院;南京晓庄学院数学与信息技术学院; |
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| 基金项目： | 国家自然科学基金项目资助(11071097) |
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| 摘 要： | 讨论弱McCoy环与相关环的关系,研究环的多项式扩张和Ore扩张的弱McCoy性,证明了:(1)设R是右Ore环,则R是右弱McCoy环当且仅当R的典范右商环Q是右弱McCoy环;(2)如果R是(α,δ)compatible的可逆环,则R［x;α,δ］是右弱McCoy环.
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| 关 键 词： | 弱McCoy环 可逆环 半交换环 环的扩张 Ore扩张 |
| 收稿时间： | 2013-06-18; |
The extensions of weak McCoy rings |
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| WANG Yao,REN Yanli,LI Xiaowei. The extensions of weak McCoy rings[J]. Journal of Zhejiang University(Sciences Edition), 2014, 41(4): 376-380. DOI: 10.3785/j.issn.1008-9497.2014.04.003 |
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| Authors: | WANG Yao REN Yanli LI Xiaowei |
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| Affiliation: | WANG Yao , REN Yanli , LI Xiaowei (1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China ; 2. School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, China) |
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| Abstract: | The relationships between weak McCoy rings and related rings are investigated, and the weak McCoy properties of the polynomial extension and Ore extension of a ring are studied. It is proved that （1）Let R be a right Ore ring and Q be the classical right quotient ring of R, then R is a weak right McCoy ring if and only if Q is a weak right McCoy ring; （2）If R be （α,δ）-compatible and reversible, then R[x;α,δ] is a right weak McCoy ring. |
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| Keywords: | weak McCoy ring reversible ring semicommutative ring~ extensions of rings Ore extension |
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