| 一般环之分式环 |
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| 引用本文： | 王伟亮,任艳丽. 一般环之分式环[J]. 数学理论与应用, 2012, 0(1): 82-86 |
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| 作者姓名： | 王伟亮 任艳丽 |
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| 作者单位： | 南京信息工程大学信息与控制学院;南京晓庄学院数学与信息技术学院 |
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| 基金项目： | 江苏省教育厅自然科学基金项目(11KJB110007);江苏省高校“青蓝工程”中青年学术带头人培养对象项目 |
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| 摘 要： | 本文给出一般环R之分式环△^-1R的构造和△^-R的理想的一些性质，推广了现有中外教科书的结论．证明了（1）△^-1R中理想有且仅有形式△^-1I，其中△3R．（2）如果P是R的素理想，且△∩P=Ф，则△^-1P是△^-1R的素理想，且θ^-1（△^-1P）=P。
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| 关 键 词： | 分式环 理想 正则元 中心元 |
On Rings of Quotients of General Rings |
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| Wang Weiliang,Ren Yanli. On Rings of Quotients of General Rings[J]. Mathematical Theory and Applications, 2012, 0(1): 82-86 |
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| Authors: | Wang Weiliang Ren Yanli |
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| Affiliation: | 1.College of Information and Cybernetics,Nanjing University of Information Science and Technology, Nanjing,210044,China)(2.College of Mathematics and Information Technology,Nanjing Xiaozhuang University,Nanjing,211171,China) |
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| Abstract: | In this note,we give the structure of the ring Δ-1R of quotients of a general ring R and some properties of ideals of Δ-1R,generalize some known results in literature.It is shown that(1) J is an ideal of Δ-1R if and only if J=Δ-1I for some I■R.(2) if P is a prime ideal of R and Δ∩P=Ф,then Δ-1P is a prime ideal of Δ-1R and θ-1(Δ-1P)=P. |
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| Keywords: | Ring of quotients Ideal Regular element Central element |
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