| Zn上四元数代数Zn[i,j,k]的零因子和单位群 |
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| 引用本文： | 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. |
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| 作者姓名： | 韦扬江 唐高华 林光科 |
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| 作者单位： | 广西师范学院数学科学学院,广西南宁,530001 |
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| 基金项目： | 国家自然科学基金，the Guangxi Science Foundation，the Innovation Project of Guangxi Graduate Education，the Scientific Research Foundation of Guangxi Educational Committee |
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| 摘 要： | 研究Zn上的四元数代数Zni,j,k]的零因子和单位群,给出Zni,j,k]的零因子个数和Zni,j,k]的单位群阶的计算公式,证明Zni,j,k]≌M2（Zn）的充分必要条件是n为奇数,并且完全决定了Zni,j,k]的单位群结构.
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| 关 键 词： | 四元数代数 零因子 单位群 |
| 收稿时间： | 2008/11/17 0:00:00 |
The Zero-divisors and the Unit Group of Quaternion Algebra Zn[i,j,k] |
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| WEI Yang-jiang,TANG Gao-hua and 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. |
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| Authors: | WEI Yang-jiang TANG Gao-hua and LIN Guang-ke |
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| Institution: | School of Mathematical Sciences;Guangxi Teachers Education University;Nanning;Guangxi;530001;China |
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| Abstract: | We investigate the zero divisors and the unit group of quaternion algebra over Zn which is denoted by Zni,j,k]≈and obtain the calculating formulas of the number of zero divisors and the order of the unit group of Zni,j,k].We prove that Zni,j,k]M2(Zn) if and only if n is odd.In addition,the structure of the unit group of Zni,j,k]are completely determined. |
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| Keywords: | quaternion algebra zero-divisor unit group |
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