Quasi-Type δ Semigroups with an Adequate Transversal

In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are characterized.Our results genera...     

On generalized inverse transversals

Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.     

Trotter—Kato Theorems for an α—times Integrated Semigroups

In this paper,we discuss on the convergence and approximation of an α-times integrated semigroups. The Trotter-kato theorems for an α-times integrated semigroups are obtained.     

Abundant semigroups with a quasi-ideal quasi-adequate transversal

Characterization theorems for abundant sernigroups having a quasi-ideal quasi-adequate transversal are obtained. Our results generalize and amplify the related results of Satio on regular semigroup obtained in 1985 and Kong obtained in 2007 respectively. Some recent results on this topic given by Guo-Shum are strengthened. In particular, the structure of such an abundant semigroup is described.     

A Class of Left E-adequate Semigroups

In this paper we establish a construction of a class of left E-adequate semigroups by using semilattices of cancellative monoids and fundamental left E-adequate semigroups. We first introduce concepts of type μ^＋（μ^＊,μ ） abundant semigroups and type μ^＋left E-adequate semigroups. In fact, regular semigroups are type μ^＋abundant semigroups and inverse semigroups are type μ^＋left E-adequate semigroups. Next, we construct a special kind of algebras called E^＋-product. It is proved that every E^＋-product is a type μ^＋left E-adequate semigroup, and every type μ^＋left E-adequate semigroup is isomorphic to an E^＋-product of a semilattice of cancellative monoids with a fundamental left E-adequate semigroup. Finally, as a corollary of the main result, it is deduced that every inverse semigroup is isomorphic to an E^＋-product of a Clifford semigroup by a fundamental inverse semigroup.     

带有乘右适当断面的右主投射半群(英文)

In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.     

序半环的序理想

An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring.     

具有逆断面的局部逆半群

Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.     

关于Wrpp半群上的Lawson偏序(英文)

In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.     

INVERSE MONOIDS OF GRAPHS

. IntroductionGraph endomorphism and its regularity property have been investigated in some literatures (of. [1--41 for examples). The invertibility is a stronger algebraic property thanregUlarity in semigroup theory. It is commonly agreed that inverse semigroups are the mostpromising class of semigroups for study. In this paper we first present a combinatorial characterization of an inverse monoid of a graph (Theorem 2.3). Then using this we prove thata bipartite graph with an inverse monoi…     

Naturally ordered regular semigroups with an inverse monoid transversal

The notion of an inverse transversal of a regular semigroup is well-known. Here we investigate naturally ordered regular semigroups that have an inverse transversal. Such semigroups are necessarily locally inverse and the inverse transversal is a quasi-ideal. After considering various general properties that relate the imposed order to the natural order, we highlight the situation in which the inverse transversal is a monoid. The regularity of Green’s relations is also characterised. Finally, we determine the structure of a naturally ordered regular semigroup with an inverse monoid transversal.     

具有某种断面的半群的研究进展

本文综述了几类具有特殊断面的半群的近期研究结果。在介绍逆半群和正则半群的一般结构之后，概述了具有逆断面的正则半群的结构和同余格的研究成果。总结了作为逆断面的推广的可裂断面，纯正断面，正则^*－断面和恰当断面。提出了可以进一步研究的重要的问题。     

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.     

具有CO-恰当断面富足半群的一种构造方法

本文首先研究了具有可消模断面的拟恰当半群的结构,然后给出了用可消模断面的拟恰当半群构造具有CO-恰当断面富足半群的方法.     

具有Clifford断面的纯正半群

本文研究有Clifford断面的纯正半群.为了获得主要的结构定理，证明了纯正半群有群断面当且仅当它是矩形群;利用半格和矩形带，建立了有Clifford断面的纯正半群的结构.     

具有拟理想正则*-断面的正则半群

本文提出了具有正则*-断面正则半群的概念，所给出的例子表明具有拟理想正则*-断面的正则半群类真包含了具有拟理想逆断面的正则半群类和正则*-半群类；最后刻画了具有拟理想正则*-断面的正则半群的结构．     

具有弱中间幂等元的正则半群

本文在正则半群上引入弱中间幂等元和拟中间幂等元,着重探讨了这两类幂等元的性质特征.构造了若干具有弱(拟)中间幂等元的正则半群,确定了弱中间幂等元和拟中间幂等元之间的关系,给出了弱中间幂等元和拟中间幂等元各自的等价判定,利用拟中间幂等元刻画了纯正半群.最后,得到了构造具有拟中间幂等元的正则半群的一般途径,并在此基础上进一步给出了判定正则半群是否具有乘逆断面的方法.     

Good congruences on abundant semigroups with multiplicative quasi-adequate transversals

In this paper, some properties of good homomorphic images of abundant semigroups with a multiplicative quasi-adequate transversal are obtained. After that, good congruences on a class of abundant semigroups with such transversals are studied. We characterize the good congruences by using the so-called good congruence triple. Furthermore, we prove that any good congruence on a class of abundant semigroups with such transversals can be constructed by the good congruence triple.     

Abundant Semigroups with a Multiplicative Adequate Transversal

The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal. Some properties and characterizations for such semigroups are obtained. In particular, we establish the structure of this class of abundant semigroups in terms of left normal bands, right normal bands and adequate semigroups with some simple compatibility conditions. Finally, we apply this structure to some special cases. Received February 25, 1999, Revised November 22, 1999, Accepted December 9, 1999     

具有Clifford断面的正则纯正半群

给出了具有Clifford断面的右正规纯正半群的等价刻画,得到了具有Clifford断面的正则纯正半群的次直积分解,证明了具有Clifford断面的正则纯正半群一定是正则纯正群．