| Gauss整数环的主理想及其商环研究 |
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| 引用本文： | 王小娟.Gauss整数环的主理想及其商环研究[J].淮阴师范学院学报(自然科学版),2011,10(6):482-486. |
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| 作者姓名： | 王小娟 |
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| 作者单位： | 新疆机电职业技术学院,新疆乌鲁木齐,830011 |
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| 摘 要： | 研究了Gauss整数环商环中元素的个数问题,并用一种新的初等方法解决了以下猜想：Gauss整数环的商环（Zi]/（n＋mi））元素个数是m2＋n2.
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| 关 键 词： | Gauss整数环 理想 商环 素元 |
Research the Principal Ideal and Quotient Ring of Gaussian Integral Domain |
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| WANG Xiao-juan.Research the Principal Ideal and Quotient Ring of Gaussian Integral Domain[J].Journal of Huaiyin Teachers College(Natrual Science Edition),2011,10(6):482-486. |
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| Authors: | WANG Xiao-juan |
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| Institution: | WANG Xiao-juan(XinJiang Mechano-Electrical Vocational and Technical Insititute,Urumqi Xinjiang 830011,China) |
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| Abstract: | The definition and some properties of the quotient ring,the unit and the simple element of Gauss integral ring are discussed,element numbers of the quotient ring of Gauss integral ring is researched,and proves one of the two conjectuires of Arch.with a new and elementary method.In light of the Gaussian integral domain,the number of elements of its ring of quotients is m2+n2. |
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| Keywords: | gauss integral ring ideal quotient ring prime element |
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