| 序半群的一类正则同余 |
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| 引用本文： | 谢祥云,郭小江. 序半群的一类正则同余[J]. 数学进展, 2007, 36(4): 459-466 |
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| 作者姓名： | 谢祥云 郭小江 |
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| 作者单位： | 1. 五邑大学数理系,江门,广东,529020
2. 江西师范大学数学与信息科学学院,南昌,江西,330027 |
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| 基金项目： | 国家自然科学基金;广东省自然科学基金 |
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| 摘 要： | 设S是有向序半群,本文给出了S上的一类正则同余,称为强序同余的定义及性质.证明了S的强序同余是强正则同余,但反之不成立.同时证明了强序同余格SOC(S)是S的同余格C(S)关于通常集合的交和传递积的V-完备的分配子格.
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| 关 键 词： | 有向序半群 强序同余 正则同余 分配格 |
| 文章编号： | 1000-0917（2007）04-0459-08 |
| 修稿时间： | 2005-05-12 |
A Class of Regular Congruences on Ordered Semigroups |
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| XIE Xiangyun,GUO Xiaojiang. A Class of Regular Congruences on Ordered Semigroups[J]. Advances in Mathematics(China), 2007, 36(4): 459-466 |
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| Authors: | XIE Xiangyun GUO Xiaojiang |
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| Abstract: | In this paper,the notation of a strongly ordered congruence on an ordered semigroup S is introduced.Some properties of strongly ordered congruences are given.The results that the strongly ordered congruences are the strongly regular congruences and that the converses are not true are proved.In the Section 3,we also prove that the set SOC(S) of all strongly ordered congruences on an ordered semigroup S is a V-complete distributive sublattice of the lattice C(S) of all congruences on S with respect to the intersection defined as usual and the union (also called transitive product). |
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| Keywords: | directed ordered semigroup strongly ordered congruence regular congruence distributive lattice |
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