| 四元数代数Z_n[i,j,k]的素谱和根(英文) |
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| 引用本文： | 韦扬江,唐高华,林光科. 四元数代数Z_n[i,j,k]的素谱和根(英文)[J]. 广西师范学院学报(自然科学版), 2009, 26(1) |
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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 Scientifc Research Foundation of Guangxi Educational Committee |
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| 摘 要： | Z n 上的四元数环Z n [i,j,k]是一个Z n 上的代数.该文研究Z n [i,j,k]的相关性质并证明Z n [i,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Z n [i,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 Z_n[i,j,k] |
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| WEI Yang-jiang,TANG Gao-hua,LIN Guang-ke. The Spectra and Radicals of Quaternion Algebra Z_n[i,j,k][J]. Journal of Guangxi Teachers Education University:Natural Science Edition, 2009, 26(1) |
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| Authors: | WEI Yang-jiang TANG Gao-hua LIN Guang-ke |
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| Affiliation: | School of Mathematical Sciences;Guangxi Teachers Education University;Nanning 530001;P.R.China |
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| Abstract: | The ring of quaternions over Z n which is denoted by Z n [i, j, k] is a quaternion algebra. In this paper, we investigate the properties of Z n [i, j, k] and it is shown that Z n [i, j, k] is a local ring if and only if n=2t with t≥1. We completely determine the maximal one-sided ideals, maximal two-sided ideals, the prime spectrum and the Jacobson radical of Z n [i, j, k]. |
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| Keywords: | quaternion algebra maximal ideal maximal one-sided ideal prime spectrum Jacobson radical |
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