| 关于Herstein猜想 |
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| 引用本文： | 周柏荣. 关于Herstein猜想[J]. 湖北师范学院学报(自然科学版), 1988, 0(1) |
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| 作者姓名： | 周柏荣 |
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| 作者单位： | Department of Mathematics，Wuhan University |
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| 摘 要： | 本文引入环的半质函数S和关于环的子集的左零化子极限链条件,并获得如下结果:设R为环,且对于R的每一幂零元α≠0均有S(α)∈N、则R的全部幂零元形成R的Baer根;设R为CN-环,T为R的全体诣零左理想之和,K为R的kthe根,则R成立Herstein猜想当且仅当R在T-K上满足左零化子极限链条件。
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| 关 键 词： | 幂零元 诣零左理想 半质函数 左零化子极限链条件 |
ON THE HERSTEIN CONJECTURE |
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| Zhou Borong. ON THE HERSTEIN CONJECTURE[J]. Journal of Hubei Normal University(Natural Science), 1988, 0(1) |
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| Authors: | Zhou Borong |
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| Abstract: | In this paper we introduce a function S for rings which is called a semiprime function and the limit chain condition for left anuihilators on subset of a ring and we get following mainresults:theorem3: Let R be a CN-ring, T be the sum of all of nil left ideals of R, K be the K(?)the radical of R. R is true for the Herstein conjecture if and only if R satisfies the limit chain condition for left annihil ators on T-K. |
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| Keywords: | nilpotent nil left ideal semiprime function limit chain condition for left annihilators |
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