The aim of this paper is to determine the subset of an ordered semigroup S that can serve as a class of some regular congruences on S. The results on semigroups without order given in [5] can be obtained as consequences.
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 F-semigroups. We can see that any ...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 F-semigroups. We can see that any semigroup can be considered as a F-semigroup. In this paper, we introduce and characterize the concept of the regular congruences OnE ordered F-semigroups and prove the following statements on an ordered F-semigroup M： （1） Every ordered semilattice congruences is a regular congruence. （2） There exists the least regular order on the F-semigroup M/p with respect to a regular congruence p on M. （3） The regular congruences are not ordered semilattice congruences in general.展开更多
基金Supported by the National Natural Science Foundation of China and NSP ofGuangdong Province (990825)
文摘The aim of this paper is to determine the subset of an ordered semigroup S that can serve as a class of some regular congruences on S. The results on semigroups without order given in [5] can be obtained as consequences.
文摘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 F-semigroups. We can see that any semigroup can be considered as a F-semigroup. In this paper, we introduce and characterize the concept of the regular congruences OnE ordered F-semigroups and prove the following statements on an ordered F-semigroup M： （1） Every ordered semilattice congruences is a regular congruence. （2） There exists the least regular order on the F-semigroup M/p with respect to a regular congruence p on M. （3） The regular congruences are not ordered semilattice congruences in general.
