| 序半群序同余的一个注记 |
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| 引用本文： | 石小平,谢祥云.序半群序同余的一个注记[J].数学研究及应用,2008,28(4):898-904. |
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| 作者姓名： | 石小平 谢祥云 |
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| 作者单位： | 南京师范大学数学系, 江苏 南京 210046; 东南大学数学系, 江苏 南京 210096;五邑大学数理系, 广东 江门 529020 |
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| 基金项目： | 国家自然科学基金(No.10626012; 103410020); 江苏省博士后科研资助计划(No.0502022B); 广东省自然科学基金(No.0501332); 广东省教育厅科学基金(No.Z03070). |
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| 摘 要： | 序半群S的什么子集可以作为S的同余类是一个重要的问题. 在文8]中,作者证明了如果序半群S的 理想$C$是$S$的某个同余类, 则$C$是凸的; 而且当$C$是强凸理想时，逆命题成立. 在本文中, 我们给出了序半群同余的一个新的构造，并证明了序半群$S$的理想$B$是$S$的某个同余类的充要条件是$B$是凸的.
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| 关 键 词： | 序半群 同余 凸理想. |
| 收稿时间： | 2006/8/31 0:00:00 |
| 修稿时间： | 2007/3/23 0:00:00 |
A Note of Order Congruences on Ordered Semigroups |
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| SHI Xiao Ping and XIE Xiang Yun.A Note of Order Congruences on Ordered Semigroups[J].Journal of Mathematical Research with Applications,2008,28(4):898-904. |
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| Authors: | SHI Xiao Ping and XIE Xiang Yun |
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| Institution: | Department of Mathematics, Nanjing Normal University, Jiangsu 210046, China; Department of Mathematics, Southeast University, Jiangsu 210096, China;Department of Mathematics and Physics, Wuyi University, Guangdong 529020, China |
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| Abstract: | Which subset of an ordered semigroup $S$ can serve as a congruence class of certain order-congruence on $S$ is an important problem. XIE Xiangyun proved that if every ideal $C$ of an ordered semigroup $S$ is a congruence class of one order-congruence on $S$, then $C$ is convex and when $C$ is strongly convex, the reverse statement is true in 2001. In this paper, we give an alternative constructing order congruence method, and we prove that every ideal $B$ is a congruence class of one order congruence on $S$ if and only if $B$ is convex. Furthermore, we show that the order relation defined by this method is ``the least' order congruence containing $B$ as a congruence class. |
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| Keywords: | ordered semigroup order congruence convex ideal |
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