Zn上四元数代数Zn[i,j,k]的零因子和单位群
Zn상사원수대수Zn[i,j,k]적령인자화단위군
The Zero-divisors and the Unit Group of Quaternion Algebra Zn[I,j,k]
  • 万方数据
    广西科学 엄서과학
    GUANGXI SCIENCES
    2009年 2期 147-150 ,共4页

    韦扬江%唐高华%林光科

    위양강%당고화%림광과

    四元数代数%零因子%单位群 四元數代數%零因子%單位群
    사원수대수%령인자%단위군
    quaternion algebra%zero-divisor%unit group
    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.
    연구Zn상적사원수대수Zn[i,j,k]적령인자화단위군,급출Zn[i,j,k]적령인자개수화Zn[i,j,k]적단위군계적계산공식,증명Zn[i,j,k]M2(Zn)적충분필요조건시n위기수,병차완전결정료Zn[i,j,k]적단위군결구.
    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.
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