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 clas...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.展开更多
基金the National Natural Science Foundation of China (Nos.10626012 103410020)+2 种基金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)
文摘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.
