For a regular semigroup with an inverse transversal, we have Saito’s structure W(I, S°, Λ, *, α,β). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of ...For a regular semigroup with an inverse transversal, we have Saito’s structure W(I, S°, Λ, *, α,β). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of congruences on the structure component parts I, S° and Λ. The structure of images of this type of semigroups is also presented.展开更多
It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular...It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.展开更多
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
基金This work is supported by Natural Science Foundation of Guangdong Province
文摘For a regular semigroup with an inverse transversal, we have Saito’s structure W(I, S°, Λ, *, α,β). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of congruences on the structure component parts I, S° and Λ. The structure of images of this type of semigroups is also presented.
基金supported by National Natural Science Foundation of China (Grant No.10571061)
文摘It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.
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.
