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Properties of Quaternion Algebra over the Real Number Field and Z_p

Properties of Quaternion Algebra over the Real Number Field and Z_p
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摘要 The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely many roots. Then the properties of quaternion algebra over Zp are discussed,and the order of its unit group is determined. Lastly,another ring isomorphism of M2（Zp） and the quaternion algebra over Zp when p satisfies some particular conditions are presented. The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely many roots. Then the properties of quaternion algebra over Zp are discussed,and the order of its unit group is determined. Lastly,another ring isomorphism of M2（Zp） and the quaternion algebra over Zp when p satisfies some particular conditions are presented.
作者 秦应兵
机构地区 School of Mathematics
出处 《Journal of Southwest Jiaotong University(English Edition)》 2010年第4期349-352,共4页 西南交通大学学报（英文版）
关键词 Quaternion algebra Quadric equation with one variable Modulo p residue class ring Unit group Ring isomorphism Quaternion algebra Quadric equation with one variable Modulo p residue class ring Unit group Ring isomorphism
分类号 O156.1 [理学—基础数学]
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参考文献8

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  • 2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):1-10. 被引量：1
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二级参考文献15

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Journal of Southwest Jiaotong University(English Edition)
2010年 第4期

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