| Gauss整环的理想和商环 |
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| 引用本文： | 卢梦霞,李红杰.Gauss整环的理想和商环[J].河南师范大学学报(自然科学版),2012,40(5):35-37. |
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| 作者姓名： | 卢梦霞 李红杰 |
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| 作者单位： | 周口师范学院数学与信息科学系,河南周口,466001 |
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| 基金项目： | 河南省科技厅项目(112300410109) |
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| 摘 要： | 主要讨论了Gauss整环Zi]的理想中的元素形式和性质,商环中的元素个数,商环的结构及商环构成域的条件.另外,给出了Gauss整环关于映射φ:a+bi→a2+b2作成一个欧氏环的两种证法.
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| 关 键 词： | 理想 商环 Gauss整环 域 |
Ideal and Quotient Ring of the Gauss Domain Z[i] |
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| LU Meng-xia
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LI Hong-jie.Ideal and Quotient Ring of the Gauss Domain Z[i][J].Journal of Henan Normal University(Natural Science),2012,40(5):35-37. |
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| Authors: | LU Meng-xia LI Hong-jie |
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| Institution: | (Department of Mathematics and Information Science,Zhoukou Normal University,Zhoukou 466001,China) |
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| Abstract: | This paper mainly talks about the element forms and properties about the ideal Gauss domain Zi],elment number and structure of quotient ring and the condition in which quotient ring constitutes field.In addition,it proves two kinds of proof of the Gauss integral ring on the mapping: φ:a+bi→a2+b2 as a Euclidean domain. |
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| Keywords: | ideal quotient ring gauss domain field |
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