| 半素PI-环的本质(单边)理想 |
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| 引用本文： | 游松发.半素PI-环的本质(单边)理想[J].数学学报,2001,44(4):747-752. |
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| 作者姓名： | 游松发 |
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| 作者单位： | 湖北大学研究生处 |
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| 摘 要： | 本文系统研究了半素ＰＩ－环本质（单边）理想及最大商环的有关性质，从ＰＩ－理论中著名的 Ｒｏｗｅｎ非平凡相交定理出发，证明了半素 ＰＩ－环的本质（单边）理想包合一个本质两边理想（定理７，推论８），建立了半素ＰＩ－环本质（单边）理想与其中心本质理想的内在联系（定理 ９，推论 １０），并以此为基础，证明了半素 ＰＩ－环的最大商环是 ＰＩ的（定理 １２），且半素 ＰＩ－环的每一正则元在其最大商环中是可逆的（定理 １４）．
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| 关 键 词： | 本质(单边)理想 奇异理想 半素PI-环 非平凡相交 最大商环 |
| 文章编号： | 0583-1431(2001)04-0747-06 |
| 修稿时间： | 1999年9月3日 |
The Essential(One-Sided) Ideals of Semiprime PI-Rings |
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| YOU Song Fa.The Essential(One-Sided) Ideals of Semiprime PI-Rings[J].Acta Mathematica Sinica,2001,44(4):747-752. |
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| Authors: | YOU Song Fa |
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| Institution: | YOU Song Fa (Section of Postgraduate, Hubei University, Wuhan 430062, P. R. China) (Fax: (027)86743060; E-mail: yjsc @dns. hubu.deu.cn) |
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| Abstract: | We research some properties on the essential (one-sided) ideals and the maximal quotient rings of smiprime PI-rings. The main resu is proved in this paper are that if R is a semiprine PI-rings then every essential one-sided ideal of R contains an essential two-sided ideal of R (Th7, Cor8), the connection between essential one sided ideals of R and essential ideals of the center are indicated (Th9 Cor10), the maximal quotient ring of R is also PI (Th12), every regular element in R is invertible in maximal quotient ring (Th14). |
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| Keywords: | Essential (one- sided) ideal Singular ideal Semiprime PI-ring Nontrivial intersect Maximal quotient |
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