| 摘要: |
| 本文引入了α-McCoy环和弱α-McCoy环的概念分别研究了一个环R关于其自同态α的McCoy性质和弱McCoy性质. 利用各种环扩张, 证明了一个环R是α-McCoy环当且仅当R[x]是α-McCoy环, 得到了正向系上弱α-McCoy 环的正向极限是弱α-McCoy环, 推广和改进了McCoy环在矩阵环和多项式上的相关结论. |
| 关键词: McCoy 环 α-McCoy环 弱α-McCoy环 |
| DOI： |
| 分类号:O153.3 |
| 基金项目:Supported by the Provincial Natural Science Research Program of Higher Education Institution of Anhui Province of China (KJ2012Z028); Partially Supported by the Foundation for Young Talents in College of Anhui Province of China (2012SQRL039); the National Natural Science Foundation of China (11226056). |
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| ON RELATIVE MCCOY PROPERTIES WITH A RING ENDOMORPHISM |
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ZHAO Liang, GU Qin-qin
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School of Mathematics & Physics, Anhui University of Technology, Maanshan 243032, China
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| Abstract: |
| In this paper, we introduce the notions of an α-McCoy ring and weak α-McCoy rings to study McCoy properties and weak McCoy properties relative to an endomorphism α of a ring R. By using various ring extensions, we prove that a ring R is a right α-McCoy ring if and only if R[x] is a right α-McCoy ring, and the direct limit of a direct system of right weak α-McCoy rings is investigated in the last section. It is shown that if R is a right weak α-McCoy ring. Some well-known results on McCoy rings are generalized. |
| Key words: McCoy rings α-McCoy rings weak α-McCoy rings |
