| 具有弱对称自同态的环 |
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| 引用本文： | 王尧,钱青,任艳丽.具有弱对称自同态的环[J].山东大学学报(自然科学版),2014(2):12-17,28. |
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| 作者姓名： | 王尧 钱青 任艳丽 |
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| 作者单位： | [1]南京信息工程大学数学与统计学院,江苏南京210044 [2]南京晓庄学院数学与信息技术学院,江苏南京211171 |
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| 基金项目： | 国家自然科学基金资助项目（11101217） |
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| 摘 要： | 推广了弱对称环的概念，研究了具有弱对称自同态α的环，称为弱对称α-环，讨论弱对称α-环与相关环的关系，研究了弱对称α-环的一些扩张性质。证明了：（1）设α是环R的自同态，则R是α-rigid环当且仅当R是弱对称α-环，且由aRα（a）∈nil（R）可推出a＝0，对任何a∈R；（2）设R是半交换环，α是R的自同态，则R是弱对称α-环当且仅当R x]是弱α珔-sy环。
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| 关 键 词： | 对称环 弱对称环 弱对称α-环 α-rigid环 |
Rings with weakly symmetric endomorphisms |
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| WANG Yao,QIAN Qing,REN Yan-li.Rings with weakly symmetric endomorphisms[J].Journal of Shandong University(Natural Science Edition),2014(2):12-17,28. |
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| Authors: | WANG Yao QIAN Qing REN Yan-li |
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| Institution: | 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China; 2. School of Mathematics and Information Technology, Nanjingxiaozhuang University, Nanjing 211171, Jiangsu, China) |
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| Abstract: | The notion of weakly symmetric α-rings, which is rings with weakly symmetric endomorphismα, is intro-duced, and the study of weakly symmetric rings is extended.The relationships between weakly symmetric α-rings and related rings are discussed and some extensions of weakly symmetricα-rings are investigated.It is showed that （1） Letαbe an endomorphism of a ring R.Then R isα-rigid if and only if R is weakly symmetricα-ring and aRα（ a）∈nil（ R） implies a=0 for any a∈R; （2） Let R be a semicommutative ring and αan endomorphism of R.Then R is weakly symmetricα-ring if and only if R x] is weakly symmetric ā-ring. |
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| Keywords: | symmetric ring weakly symmetric ring weakly symmetricα-ring α-rigid ring |
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