半群断面的同构

我们首先证明，若S^*,S^o是正则半群S的两个纯正断面，σ^*,σ^o分别是S^*,S^o上的最小逆半群同余，则商半群S^*/σ^o同构。作为上述结论的一个推论，重新获得：含逆断面的正则半群的所有逆断面均同构。关于富足半群我们证明了：满足正则性条件的富足半群若含有似理想恰当断面，则其所有拟理想恰当断面均同构。     

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.     

具有左单S-恰当断面的富足半群的结构(英文)

本文得到具有左单恰当断面的富足半群的进一步刻画.推广并丰富了Blyth和AlmeidaSantos于1996年得到的关于左单逆断面及两位作者分别于2008年与2010年得到的关于恰当断面的相关结果.建立了具有左单S-恰当断面的富足半群的结构.     

具有弱正规幂等元的富足半群的结构

本文研究含弱正规幂等元的富足半群.在给出这类半群的若干特征后,建立了具有弱正规幂等元的富足半群的结构．作为应用,给出具有正规幂等元的富足半群和具有（弱）正规幂等元的拟适当半群的结构．     

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。     

富足半群上的F-好同余

引入了富足半群上F-好同余的概念,给出了富足半群上F-好同余的性质和特征.在此基础上,得到了富足半群上F-好同余的并为F-好同余的相关条件.最后,进一步对拟适当半群上的F-好同余作了讨论并得到了一些性质.     

具有E—逆断面的正则半群的结构定理

讨论了具有E－逆断面的正则半群的性质;并给出了具有E－逆断面的正则半群的一种结构定理。     

具有逆断面的左半正规纯正半群

左半正规纯正半群是幂等元集形成左半正规带的纯正半群．本文讨论了具有逆断面的左半正规纯正半群上的一些性质；给出该类半群的一个构造定理。     

具有拟理想恰当断面的富足半群

利用格林*-关系刻画R和L并给出与它们相关的一些性质.利用R和L,得到恰当断面是拟理想的几个等价条件.最后,用两个结构构件R和L给出具有拟理想恰当断面的富足半群的一个结构定理.它比陈建飞在2000年给出的要简单.     

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.     

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.     

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.     

<Emphasis Type="Italic">E</Emphasis>-inversive Dubreil-Jacotin semigroups

Using group congruences, we obtain necessary and sufficient conditions for an ordered E-inversive semigroup to be a Dubreil-Jacotin semigroup. We also determine when such a semigroup is naturally ordered. In particular, when the subset of regular elements is a subsemigroup it contains a multiplicative inverse transversal.     

基半群为0-J-严格单半群的零直并的代数

设Ａ是代数闭域ｋ上的一个具乘基Ｂ的有限维含幺结合代数，称半群Ｂ∪｛０｝为Ａ的基半群．本文给出了０ Ｊ 严格单半群的定义．对于基半群为０ Ｊ 严格单半群的零直并的代数，完全研究了它的代数表示型     

On Inverse Transversals of Ordered Regular Semigroups

We first consider an ordered regular semigroup S in which every element has a biggest inverse and determine necessary and sufficient conditions for the subset S ^○ of biggest inverses to be an inverse transversal of S. Such an inverse transversal is necessarily weakly multiplicative. We then investigate principally ordered regular semigroups S with the property that S ^○ is an inverse transversal. In such a semigroup we determine precisely when the set S ^☆ of biggest pre-inverses is a subsemigroup and show that in this case S ^☆ is itself an inverse transversal of a subsemigroup of S. The ordered regular semigroup of 2 × 2 boolean matrices provides an informative illustrative example. The structure of S, when S ^☆ is a group, is also described.     

Finite union of commutative power joined semigroups

A commutative semigroup is called power joined if for every element a, b there are positive integers m, n such that a^m=bⁿ. A commutative power joined semigroup is archimedean (p. 131, [3]) and cannot be decomposed into the disjoint union of more than one subsemigroup. Every commutative semigroup is uniquely decomposed into the disjoint union of power joined subsemigroups which are called the power joined components. This paper determines the structure of commutative archimedean semigroups which have a finite number of power joined components. The number of power joined components of commutative archimedean semigroups is one or three or infinity. The research for this paper was supported in part by NSF Grant GP-11964.