| 自内射环的余Hopf性 |
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| 引用本文： | 郝志峰,冯良贵.自内射环的余Hopf性[J].数学研究及应用,2001,21(2):203-206. |
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| 作者姓名： | 郝志峰 冯良贵 |
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| 作者单位： | 1. 华南理工大学应用数学系,
2. 国防科技大学七系, |
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| 基金项目： | Supported by the Natural
Science Foundation of China (19901009) |
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| 摘 要： | 本文证明了自内射环R是余Hopf的当且仅当R满足stablerangeone.于是得到了Varadarajan在9]中的公开总是对于自内射环是成立的，即Mn(R)是余Hopf的当且仅当R是余Hopf的.作为应用证明了Goodeal的一个公开问题对于自内射正则环有肯定的回答.
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| 关 键 词： | 自内射环 余Hopf性 结合环 |
| 文章编号： | 1000-341X(2001)02-0203-04 |
| 收稿时间： | 4/6/1998 12:00:00 AM |
| 修稿时间： | 1998年4月6日 |
CoHopficity of Self-Injective Rings |
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| HAO Zhi-feng and FENG Liang-gui.CoHopficity of Self-Injective Rings[J].Journal of Mathematical Research with Applications,2001,21(2):203-206. |
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| Authors: | HAO Zhi-feng and FENG Liang-gui |
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| Institution: | Dept. of Appl. Math., South China University of Technology, Guangzhou 510641, China;Dept. of Sys. & Eng. Math., National Univ. of Defence Tech., Changsha 410073, China |
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| Abstract: | It is shown that a self-injective ring R is coHofian ring if and only if R has stable range one. This answers the open problem 5 of Varadarajian in 9] for selfinjective ring R,i.e.,Mn(R) is coHopfian for coHopfian ring R. As a consequence of we answer problem of Goodeal in the affirmative in 3], for self-injective regular rings. |
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| Keywords: | coHopfian rings self-injective rings stable range one |
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