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引用本文：

韦扬江,唐高华,林光科.Z_n上四元数代数Z_n[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 Z_n[i,j,k][J].Guangxi Sciences,2009,16(2):147-150. [点击复制]

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*Z_n上四元数代数Z_n[i,j,k]的零因子和单位群*
韦扬江, 唐高华, 林光科
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(广西师范学院数学科学学院, 广西南宁 530001)

摘要:

研究Z_n上的四元数代数Z_n[i,j,k]的零因子和单位群,给出Z_n[i,j,k]的零因子个数和Z_n[i,j,k]的单位群阶的计算公式,证明Z_n[i,j,k]≌M₂(Z_n)的充分必要条件是n为奇数,并且完全决定了Z_n[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).

The Zero-divisors and the Unit Group of Quaternion Algebra Z_n[i,j,k]

WEI Yang-jiang, TANG Gao-hua, LIN Guang-ke

(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 Z_n which is denoted by Z_n[i,j,k] and obtain the calculating formulas of the number of zero-divisors and the order of the unit group of Z_n[i,j,k].We prove that Z_n[i,j,k]≌M₂(Z_n) if and only if n is odd.In addition,the structure of the unit group of Z_n[i,j,k] are completely determined.

Key words: quaternion algebra zero-divisor unit group

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