| 半素PI-环的正则元 |
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| 引用本文： | 游松发.半素PI-环的正则元[J].湖北大学学报(自然科学版),2010,32(4):351-353. |
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| 作者姓名： | 游松发 |
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| 作者单位： | 湖北大学数学与计算机科学学院,湖北武汉430062 |
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| 摘 要： | 考察半素PI-环的左、右正则元,得到如下3个方面的结果:(1)半素PI-环的左正则元一定是右正则的;(2)半素PI-环R的正则元a所生成的左理想Ra在R中是本质的,且Ra与R满足相同的多项式恒等式;(3)半素PI-环的正则元在其有1的商环中是可逆的.
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| 关 键 词： | 半素PI-环 正则元 奇异理想 本质理想 Neumann-正则 |
Regular elements in semiprime PI-rings |
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| YOU Songfa.Regular elements in semiprime PI-rings[J].Journal of Hubei University(Natural Science Edition),2010,32(4):351-353. |
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| Authors: | YOU Songfa |
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| Institution: | YOU Songfa (School of Mathematics and Computer Science,Hubei University,Wuhan 430062,China) |
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| Abstract: | An investigation on left and right regular elements of semiprime PI-rings was made,and obtained three results：（1）The left regular element was the right regular in semiprime PI-ring;（2）The left ideal Ra of regular element a in semiprime PI-rings was essential;and R and Ra satisfies the same polynomial identities;（3）The regular element in semiprime PI-ring R was invertible in the maximal left quotient ring of R. |
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| Keywords: | semiprime PI-ring regular element singular ideal essential ideal Neumann-regular |
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