| 环上的拓扑和偏序 |
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| 引用本文： | 罗淑珍,赖新兴,偶世坤.环上的拓扑和偏序[J].模糊系统与数学,2012,26(4):149-154. |
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| 作者姓名： | 罗淑珍 赖新兴 偶世坤 |
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| 作者单位： | 江西理工大学理学院,江西赣州,341000 |
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| 基金项目： | 江西省教育厅青年科学基金资助项目，江西理工大学校级科研项目 |
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| 摘 要： | 在环R上引入了拓扑OR]和偏序≤R,证明了(R,OR])是可分的,第一可数的局部紧空间,并得出了如下结论:(1)(R*,O*R])是T1的当且仅当O*R]是离散的当且仅当R中的任一元r满足r=r2=-r;(2)若(R,OR])是T0的,则U∈OR]当且仅当U=↓U;(3)若R是伪有限的且对任意r都有〈r〉>2,则(R,≤R)是代数Domain;(4)若环R的特征数chR为2,则R是伪有限的当且仅当Rop是代数Domain。
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| 关 键 词： | 环 环拓扑 环偏序 代数domain |
Topologies and Orders on Rings |
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| LUO Shu-zhen
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LAI Xin-xing
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OU Shi-kun.Topologies and Orders on Rings[J].Fuzzy Systems and Mathematics,2012,26(4):149-154. |
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| Authors: | LUO Shu-zhen LAI Xin-xing OU Shi-kun |
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| Institution: | (Faculty of Science,Jiangxi University ofScience and Technology,Ganzhou 341000,China),China) |
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| Abstract: | In this paper,we introduce the topology OR] and the partial order ≤R on rings R,prove that the topology spaces(R,OR]) are separabl,first-countable and locally compact space;get the following results:(1) if rings R is pseudo-finite and r∈R,|〈r〉|>2,then(R,≤R) is algebraic domain;(2) (R*,O*R]) is a T1-space iff O*R] is discrete iff r∈R*,r=r2=-r;(3) if(R,OR]) is a T0-space,then U∈OR] iff U=↓U;(4) if chR=2,then R is pseudo-finite iff Rop is algebraic domain. |
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| Keywords: | Ring Ring Topology Ring Partial Order Algebraic Domain |
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