序半群的正则同余类的注记

Remarks on Regular Congruence Classes of Ordered Semigroups

什么样的子集可以作为一个序半群的正则同余的同余类仍是一个公开问题．Ｋｅｈａｙｏｐｕｌｕ和Ｔｓｉｎｇｅｌｉｓ给出了什么样的子集可以作为序半群的某个正则半格同余的同余类．继他们之后，本文证明了序半群Ｓ的半群结构上的理想Ｃ是Ｓ的正则同余类的充分必要条件为Ｃ是凸集．

What subsets of an ordered semigroup S can serve as a congruence class of certain regular congruence on S is still an open problem to be solved. Kehayopulu and Tsingeles have given out a characterization whose subsets of S are a congruence class of some regular semilattice congruence on S . The aim of this paper is to prove that an ideal C of an ordered semigroup S on its semigroup structure can serve as a class of some regular congruences on S if and only if C is convex.