| 引用本文： |
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韦扬江,唐高华,林光科.Zn上四元数代数Zn[i,j,k]的零因子和单位群[J].广西科学,2009,16(2):147-150. [点击复制]
- WEI Yang-jiang,TANG Gao-hua,LIN Guang-ke.The Zero-divisors and the Unit Group of Quaternion Algebra Zn[i,j,k][J].Guangxi Sciences,2009,16(2):147-150. [点击复制]
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| 摘要: |
| 研究Zn上的四元数代数Zn[i,j,k]的零因子和单位群,给出Zn[i,j,k]的零因子个数和Zn[i,j,k]的单位群阶的计算公式,证明Zn[i,j,k]≌M2(Zn)的充分必要条件是n为奇数,并且完全决定了Zn[i,j,k]的单位群结构. |
| 关键词: 四元数代数 零因子 单位群 |
| DOI： |
| 投稿时间：2008-11-17 |
| 基金项目:Supported by the National Natural Science Foundation of China (10771095),the Guangxi Science Foundation (0832107,0640070),the Innovation Project of Guangxi Graduate Education (2007106030701M 15) and th e Scientific Research Foundation of Guangxi Ed ucational Committee (200707 LX233). |
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| The Zero-divisors and the Unit Group of Quaternion Algebra Zn[i,j,k] |
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WEI Yang-jiang, TANG Gao-hua, LIN Guang-ke
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| (School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, Guangxi, 530001, China) |
| Abstract: |
| We investigate the zero-divisors and the unit group of quaternion algebra over Zn which is denoted by Zn[i,j,k] and obtain the calculating formulas of the number of zero-divisors and the order of the unit group of Zn[i,j,k].We prove that Zn[i,j,k]≌M2(Zn) if and only if n is odd.In addition,the structure of the unit group of Zn[i,j,k] are completely determined. |
| Key words: quaternion algebra zero-divisor unit group |
