| 诱导算子与UMT整环 |
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| 引用本文： | 王芳贵.诱导算子与UMT整环[J].四川师范大学学报(自然科学版),2004,27(1):1-9. |
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| 作者姓名： | 王芳贵 |
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| 作者单位： | 四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 基金项目： | 国家自然科学基金 (1 0 2 71 0 52 )，四川省科技厅应用基础研究基金资助项目 |
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| 摘 要： | 设R包含于T是整环扩张，定义了T上的由R的ω-算子所诱导的星型算子ωR，并给出了ωR-乘法整环的特征．也讨论了环的ω-整相关理论与环的ω-整闭包，证明了在ω-整扩张下，环R的ω-维数与环T的ωR-维数的一致性．还证明了一个整环R是UMT整环当且仅当R的ω-整闭包R^ω是ωR-乘法整环．
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| 关 键 词： | GV-理想 ω-理想 UMT-整环 |
On Induced Operations and UMT-domains |
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| Abstract.On Induced Operations and UMT-domains[J].Journal of Sichuan Normal University(Natural Science),2004,27(1):1-9. |
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| Authors: | Abstract |
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| Abstract: | Let RT be an extension of domains. In this paper we introduce the star-operation w_R of T induced by w-operation over R and obtain some characterizations of a w_R-multiplication domain. We discussion the w-integral dependence of an extension of rings and the w-integral closure of an extension of rings, and prove that R is a UMT-domain if and only if the w-integral closure R~w of R is a w_R-multiplication domain on the star-operation w of R~w induced by the w-operation of R. |
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| Keywords: | GV-ideal w-ideal PVMD UMT-domain |
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