| 四元数代数Zn[i，j，k]的素谱和根 |
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| 引用本文： | 韦扬江,唐高华,林光科.四元数代数Zn[i，j，k]的素谱和根[J].广西师院学报,2009(1):1-10. |
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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： | This research was supported by the National Natural Science Foundation of China （10771095）, the Guangxi Science Foundation（0575052, 0640070, 0832107）, the Innovation Project of Guangxi Graduate Education（2007106030701M15） and the Scientifc Research Foundation of Guangxi Educational Committee（ 200707LX233）. |
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| 摘 要： | 磊上的四元数环Zni，j，k]是一个Zn上的代数．该文研究Zni，j，k]的相关性质并证明Zni，j，k]是一个局部环当且仅当n为2的方幂．并且，完全确定了Zni，j，k]的极大单边理想，极大双边理想，素谱和Jacobson根．
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| 关 键 词： | 四元数代数 极大理想 极大单边理想 素谱 Jacobson根 |
The Spectra and Radicals of Quaternion Algebra Zn [ i,j, k ] |
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| WEI Yang-jiang,TANG Gao-hua,LIN Guang-ke.The Spectra and Radicals of Quaternion Algebra Zn [ i,j, k ][J].Journal of Guangxi Teachers College(Natural Science Edition),2009(1):1-10. |
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| Authors: | WEI Yang-jiang TANG Gao-hua LIN Guang-ke |
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| Institution: | (School of Mathematical Sciences, Guangxi Teachers Education University,Nanning 530001, P. R. China) |
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| Abstract: | The ring of quaternions over Zn which is denoted by Zni, j, k] is a quaternion algebra. In this paper, we investigate the properties of Zn i, j, k ] and it is shown that Zn i, j, k ] is a local ring if and only if n = 2＇ with t ≥1. We oompletdy determine the maximal one- sided ideals, maximal two- sided ideals, the prime spectrum and the Jacobson radical of Zn i, j, k ]. |
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| Keywords: | quaternion algebra maximal ideal maximal one-sided ideal prime spectrum Jacobson radical |
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