The least regular order with respect to a regular congruence on ordered 螕-semigroups

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• 作者：Manoj Siripitukdet (1) manojs@nu.ac.th
  Aiyared Iampan (1) aiyared.ia@up.ac.th
• 关键词：Ordered semigroup &#8211 ; (ordered) Γ ; semigroup &#8211 ; regular congruence &#8211 ; ordered semilattice congruence and (least) regular order
• 刊名：Acta Mathematica Sinica
• 出版时间：May 2012
• 出版年：2012
• 期刊代码：2_1439-8516
• 类别：mat
• 卷：28
• 期：5
• 页码：975-982
• 数据来源：sp

摘要

The motivation mainly comes from the conditions of congruences to be regular that are of importance and interest in ordered semigroups. In 1981, Sen has introduced the concept of the Γ-semigroups. We can see that any semigroup can be considered as a Γ-semigroup. In this paper, we introduce and characterize the concept of the regular congruences on ordered Γ-semigroups and prove the following statements on an ordered Γ-semigroup M: (1) Every ordered semilattice congruences is a regular congruence.