| Triangular Matrix Representations of Rings of Generalized Power Series |
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| 引用本文： | Zhong Kui LIU. Triangular Matrix Representations of Rings of Generalized Power Series[J]. 数学学报(英文版), 2006, 22(4): 989-998. DOI: 10.1007/s10114-005-0555-z |
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| 作者姓名： | Zhong Kui LIU |
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| 作者单位： | Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China |
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| 基金项目： | Supported by National Natural Science Foundation of China （10171082）, the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China, and TRAP0YT |
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| 摘 要： | Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either （S,≤） satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].
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| 关 键 词： | 广义三角矩阵表征 扭转 PWP环 功率级数 |
| 收稿时间： | 2003-03-21 |
| 修稿时间： | 2003-03-212003-10-10 |
Triangular Matrix Representations of Ringsof Generalized Power Series |
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| Zhong Kui Liu. Triangular Matrix Representations of Ringsof Generalized Power Series[J]. Acta Mathematica Sinica(English Series), 2006, 22(4): 989-998. DOI: 10.1007/s10114-005-0555-z |
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| Authors: | Zhong Kui Liu |
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| Affiliation: | (1) Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China |
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| Abstract: | Let R be a ring and S a cancellative and torsion–free monoid and ≤ a strict order on S. If either (S, ≤) satis.es the condition that 0 ≤ s for all s ∈¸ S, or R is reduced, then the ring [[R S , ≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R S , ≤]]. |
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| Keywords: | Generalized triangular matrix representation Twisted generalized power series ring PWPring Triangulating dimension |
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