| 关于代数整数与代数数的一个注记 |
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| 引用本文： | 徐丽媛,陈良云. 关于代数整数与代数数的一个注记[J]. 东北师大学报(自然科学版), 2011, 43(3): 151-153 |
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| 作者姓名： | 徐丽媛 陈良云 |
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| 作者单位： | 白城师范学院数学系,吉林白城,137000;东北师范大学数学与统计学院,吉林长春,130024 |
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| 基金项目： | 吉林省自然科学基金资助项目(20101564); 吉林省教育厅科研项目(吉教合字2010第128号) |
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| 摘 要： | 证明了代数数是有理数系数方阵的特征值,代数整数是整数系数方阵的特征值.由此出发,完全用线性代数与矩阵计算的方法简洁地证明了代数整数对加减法和乘法封闭,从而构成一个环(代数整数环);所有代数数对加减乘除封闭,从而构成一个域(代数数域).
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| 关 键 词： | 代数数 代数整数 特征值 |
A note about algebric integer and algebra number |
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| XU Li-yuang,CHENG Liang-yun. A note about algebric integer and algebra number[J]. Journal of Northeast Normal University (Natural Science Edition), 2011, 43(3): 151-153 |
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| Authors: | XU Li-yuang CHENG Liang-yun |
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| Affiliation: | XU Li-yuang1,CHENG Liang-yun2(1.School of Mathematics,Baicheng Normal College,Baicheng 137000,China,2.School of Mathematics and Staistics,Northeast Normal University,Changchun 130024,Chian) |
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| Abstract: | In this paper,it is proved that an algebraic number can be seen as an eigenvalue of a matrix over rational field,and an algebraic integer can be seen as an eigenvalue of a matrix over integral ring.Then the important conclusion in mathematics that all algebraic integers form a ring and the field of its fractions is an algebraic number field is directly and clearly proved,in history the prove of this conclusion is much difficult for people to understand. |
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| Keywords: | algebraic number algebraic integer eigenvalu |
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