In order to study rpp semigroups, in particular, some special cases, several facts on （l）-Green’s relations and strongly rpp semigroups are given as some remarks.
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The research of the second author was supported by the NSFC (10871161)
文摘In order to study rpp semigroups, in particular, some special cases, several facts on （l）-Green’s relations and strongly rpp semigroups are given as some remarks.
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.
