| Malcev-Neumann环的主拟Baer性质 |
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| 引用本文： | 刘仲奎.Malcev-Neumann环的主拟Baer性质[J].数学杂志,2005,25(3):237-244. |
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| 作者姓名： | 刘仲奎 |
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| 作者单位： | 西北师范大学数学系,甘肃,兰州,730070 |
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| 基金项目： | SupportedbyNationalNaturalScienceFoundationofChina(10171082)andbytheTeachingandResearchAwardProgramforOutstandingYoungTeachersinHigherEducationInstitutionsofMOE,P.R.C. |
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| 摘 要： | 设R是环，G是偏序群，σ是从G到R的自同构群的映射。本文研究了Malcev-Neumann环R*((G))是主拟Baer环的条件。证明了如下结果：如果R是约化环并且σ是弱刚性的，则R*((G))是主拟Baer环当且仅当R是主拟Baer环，并且I(R)的任意G可标子集在I(R)中具有广义并．
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| 关 键 词： | Malcev-Neumann环 主拟Baer环 约化环 |
PRINCIPAL QUASI-BAERNESS OF MALCEV-NEUMANN RINGS |
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| LIU Zhong-kui.PRINCIPAL QUASI-BAERNESS OF MALCEV-NEUMANN RINGS[J].Journal of Mathematics,2005,25(3):237-244. |
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| Authors: | LIU Zhong-kui |
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| Abstract: | Let R be a ring, G an ordered group and σ a map from G into the group of automorphisms of R. The conditions under which the Malcev-Neumann ring R*((G)) is a principal quasi-Baer ring are investigated in this paper. It is shown that if R is reduced and σ is weakly rigid, then R*((G)) is right p.q.Baer if and only if R is right p.q.Baer and any G-indexed subset of I(R) has a generalized join in I(R). |
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| Keywords: | Malcev-Neumann rings principal quasi-Baer rings reduced rings |
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