| 六元gcd封闭集上Smith矩阵的整除性 |
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| 引用本文： | 赵建容,赵伟,李懋.六元gcd封闭集上Smith矩阵的整除性[J].数学学报,2011(4). |
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| 作者姓名： | 赵建容 赵伟 李懋 |
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| 作者单位： | 西南财经大学经济数学学院;现代通信国家重点实验室;西南大学数学与统计学院; |
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| 基金项目： | 中央高校基本科研业务费专项资金资助项目(XDJK2010C058) |
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| 摘 要： | 我们给出了关于六元gcd封闭集S的充分必要条件,使得在整数矩阵环M_6(Z)中,定义在S上的e次幂GCD矩阵(S~e)整除e次幂LCM矩阵S~e].这部分解决了Hong在2002年提出的一个公开问题.
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| 关 键 词： | 整除 Smith矩阵 gcd封闭集 |
Divisibility Properties of Smith Matrices on the Gcd-Closed set S with |S|=6 |
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| Jian Rong ZHAO School of Economic Mathematics,Southwestern University of Finance , Economics,Chengdu ,PR.China Wei ZHAO State Key Laboratory for Modern Communications,Chengdu ,P.R.China Mao LI School of Mathematics , Statistics,Southwest University,Chongqing ,P.R.China.Divisibility Properties of Smith Matrices on the Gcd-Closed set S with |S|=6[J].Acta Mathematica Sinica,2011(4). |
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| Authors: | Jian Rong ZHAO School of Economic Mathematics Southwestern University of Finance Economics Chengdu PRChina Wei ZHAO State Key Laboratory for Modern Communications Chengdu PRChina Mao LI School of Mathematics Statistics Southwest University Chongqing PRChina |
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| Affiliation: | Jian Rong ZHAO School of Economic Mathematics,Southwestern University of Finance and Economics,Chengdu 610074,PR.China Wei ZHAO State Key Laboratory for Modern Communications,Chengdu 610041,P.R.China Mao LI School of Mathematics and Statistics,Southwest University,Chongqing 400715,P.R.China |
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| Abstract: | In this paper,we give the necessary and sufficient conditions on the gcd- closed set S with |S| = 6 such that the power GCD matrix(S~e) divides the power LCM matrixS~e]in the ring M_n(Z) ofn×n matrices over the integers.This solves partially an open question raised by Hong in 2002. |
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| Keywords: | divisibility Smith matrix gcd-closed set |
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