Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel nor...Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel normal system; conversely any P-kernel normal system of S（P） can determine a strong P-congruence.展开更多
The necessary and sufficient conditions for the semidirect products of two monoids to be left strongly π-inverse are determined. Furthemore,the least group congruence on a strongly π-inverse semidirect is dicussed,a...The necessary and sufficient conditions for the semidirect products of two monoids to be left strongly π-inverse are determined. Furthemore,the least group congruence on a strongly π-inverse semidirect is dicussed,and some important isomorphism theorems are accessed.展开更多
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.
Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-...Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p｜s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.展开更多
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
文摘Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel normal system; conversely any P-kernel normal system of S（P） can determine a strong P-congruence.
文摘The necessary and sufficient conditions for the semidirect products of two monoids to be left strongly π-inverse are determined. Furthemore,the least group congruence on a strongly π-inverse semidirect is dicussed,and some important isomorphism theorems are accessed.
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Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p｜s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.
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.
