Split quasi-adequate semigroups

The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by McAlister and Blyth on split orthodox semigroups.     

Split Left GC-Lpp Semigroups

A left GC-lpp semigroup S is called split if the natural homomorphism γb of S onto S/γ induced by γ is split.It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal.In particular,a construction theorem for split left GC-lpp semigroups is established.     

Almost Factorizable Weakly Ample Semigroups

An appropriate generalization of the notion of permissible sets of inverse semigroups is found within the class of weakly ample semigroups that allows us to introduce the notion of an almost left factorizable weakly ample semigroup in a way analogous to the inverse case. The class of almost left factorizable weakly ample semigroups is proved to coincide with the class of all (idempotent separating) (2, 1, 1)-homomorphic images of semigroups W(T, Y) where Y is a semilattice, T is a unipotent monoid acting on Y, and W(T, Y) is a well-defined subsemigroup in the respective semidirect product that appeared in the structure theory of left ample monoids more than ten years ago. Moreover, the semigroups W(T, Y) are characterized to be, up to isomorphism, just the proper and almost left factorizable weakly ample semigroups.     

可分裂的左GC-lpp半群

A left GC-lpp semigroup S is called split if the natural homomorphism γb of S onto S/γ induced by γ is split.It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal.In particular,a construction theorem for split left GC-lpp semigroups is established.     

纯正的群的正则带的构造

本文研究纯正的群的正则带.在给出这类半群的若干特征后,建立了纯正的群的正则带的构造定理.作为应用,同时给出了纯正的群的右拟正规带的构造定理.     

Abundant semigroups with a multiplicative quasi-adequate transversal

The concept of quasi-adequate transversals is introduced. Some properties and characterizations for abundant semigroups with a multiplicative quasi-adequate transversal are obtained. In particular, a structure theorem for such abundant semigroups is given. Finally, some special cases are considered. This research was partially supported by the National Natural Science Foundation of China (No. 10571077) and the Natural Science Foundation of Gansu Province (No. 3ZS052-A25-017).     

On a Class of Subdirect Products of Left and Right Clifford Semigroups

Abstract

Regular semigroups S with the property eS ? Se or Se ? eS for all idempotents e ∈ S include all left and right Clifford semigroups. Characterizations of such semigroups are given and their structure investigated, in particular in terms of spined products of left and right Clifford semigroups with respect to Clifford semigroups.     

Abel正则球与完全正则半群

本文分别讨论了关于结合环和半群的二个定理，并且由结合环的这二个定理推出了如下准则：结合环Ｒ是Ａｂｅｌ正则的，当且仅当Ｒ的每个拟理想是正则环．     

On the Construction of Regular Orthocryptogroups

The aim of this paper is to study regular orthocryptogroups. After obtaining some characterizations of such semigroups, we establish the construction theorem of regular orthocryptogroups. As an application, we give the construction theorem of right quasi-normal orthocryptogroups and study homomorphisms between two regular orthocryptogroups. Received September 24, 1999, Accepted May 9, 2001     

On the Multiplicative Quasi-Adequate Transversals of an Abundant Semigroup

In this article, we explore the multiplicative quasi-adequate transversals of an abundant semigroup. Let S be an abundant semigroup with multiplicative quasi-adequate transversals. Then the product of any two multiplicative quasi-adequate transversals is also a multiplicative quasi-adequate transversal. Moreover, all multiplicative quasi-adequate transversals of S form a rectangular band. Let S°and S ^? be multiplicative quasi-adequate transversals of S, and let δ°(δ^?) be the δ-relation on S°(S ^?). Then there exists a bijection ? from S°/δ°onto S ^?/δ^?. In particular, if δ°and δ^? are congruences, then the bijection ? is an isomorphism.     

Structure globale des extensions regulieres galoisiennes

A natural characterization of known types of inverse transversal leads to the introduction of several new types, which we characterize in a similar natural way. Relations between the various types produce a general classification. We also determine for which types of inverse transversal considered the congruence extension property holds.     

INVERSE TRANSVERSALS ARE MUTUALLY ISOMORPHIC

It has been suspected for some time that if a regular semigroup S has an inverse transversal then all inverse transversals of S are isomorphic. Here we give a proof of this fact.     

Finitely Generated Commutative Regular Semigroups

Abstract

In this paper we give a construction that allows us to describe up to isomorphisms all finitely generated regular commutative semigroups.     

Congruence triples on regular semigroups and their generalizations

In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by using the equivalences on S/ℒ, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.     

Globals of Idempotent Semigroups

If S is a semigroup, the global (or the power semigroup) of S is the set P(S) of all nonempty subsets of S equipped with a naturally defined multiplication. A class K of semigroups is globally determined if any two semigroups of K with isomorphic globals are themselves isomorphic. We study properties of globals of idempotent semigroups and show, in particular, that the class of normal bands is globally determined.