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 |
自内射环的余Hopf性 |
CoHopficity of Self-Injective Rings |
投稿时间:1998-04-06 |
DOI:10.3770/j.issn:1000-341X.2001.02.008 |
中文关键词: |
英文关键词:coHopfian rings self-injective rings stable range one. |
基金项目: |
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中文摘要: |
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. |
英文摘要: |
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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