A Note of Order Congruences on Ordered Semigroups  

序半群序同余的一个注记(英文)

作　　者：石小平 谢祥云 

机构地区：[1]Department of Mathematics, Nanjing Normal University [2]Department of Mathematics, Southeast University [3]Department of Mathematics and Physics, Wuyi University

出　　处：《Journal of Mathematical Research and Exposition》2008年第4期898-904,共7页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China (Nos.10626012; 103410020);the Jiangsu Planned for Postdoctoral Research Found (No.0502022B);the Natural Science Foundation of Guangdong Province (No.0501332);the Educational Department Natural Science Foundation of Guangdong Province (No.Z03070)

摘　　要：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 ...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.

关 键 词：ordered semigroup order congruence convex ideal. 

分 类 号：O152.7[理学—数学]