具有Q-正则*-断面的正则半群上的*-同余格

文中给出了一个具有正则*-断面正则半群的例子,该半群同时存在非平凡*-同余和非平凡的非*-同余;证明了正则*-断面上的每个*-同余都能扩张成整个半群上的*-同余;刻划了*-同余和*-同余格;定义了*-同余格上的两个完全同余T*FS和T*S*;研究了*-同余格上的完全同余T*S*, T*, T*l, Tr, U*和V*, 给出了这些同余的类中的极值同余(除U*, V*外).     

|C(S)/L|≤2的完全正则半群

刻画了|C(S)/L|≤2的完全正则半群S的同余格的具体特征,给出了具有上述性质的所有完全正则半群的分类.     

含幺Clifford半群上的Rees矩阵半群的同余和正规加密群结构

给出了含幺Clifford半群上的Rees矩阵半群S的正规加密群结构,证明了在含幺Clifford半群上的Rees矩阵半群S上以下两个条件是等价的:(1)S上的同余ρ是完全单半群同余;(2)S上的同余ρ和S上的相容组之间存在保序双射.最后还证明了S上的完全单半群同余所构成的同余格是半模的.     

P-反演半群上的正则P-同余

令S(P)为P-反演半群，本文借助于P-核正规系来刻画S(P)上的强P-同余，证明了S(P)上的任一正则P-同余可以决定S(P)的一个P-核正规系；反之，S(P)的任一P-核正规系可以决定S(P)上的一个正则P-同余．     

|()(S)/L |≤2的完全正则半群

刻画了|(め)(S)/L|≤2的完全正则半群S的同余格的具体特征,给出了具有上述性质的所有完全正则半群的分类.     

含幺逆半群的半格上的同余格

本文证明了含幺逆半群Sα（α∈Y）的半格的容许同余格同构于半格S上同余格的一个子格。     

纯正半群上的强同余及其格

给出了纯正半群S的强同余格上同余T的一些判别性质,证明了S上所有基础强同余所构成的集合FCP（S）是CP（S）的完备子格,最后讨论了由纯正半群的正规子半群决定的交完备子格的结构及由“求核”运算确定的（交完备格）同余K的若干性质,还顺带讨论了群同余格.     

强ρ-正则半群上的最小正则*-半群同余

主要研究了强P-正则半群S(P)上的最小正则*-半群同余.利用S(P)的正则*-断面S°得到S(P)上最小正则*-半群同余的简单形式γP·由于S(P)/γp同构于S°,实质上S°是S(P)的最大正则*-半群同态象,且S(P)的正则*-断面不唯一,但从同意义上看正则*-断面唯一.     

同余自由的具有Q-逆断面的正则半群

本文讨论具有逆断面的正则半群的同余格对于它本身结构的影响．　我们给出了这类半群有最简单的同余格，即只有平凡同余的充分必要条件．     

M.Petrich和N.R.Reilly一个问题的证明

证明了M.Petrich和N.R.Reilly关于完全正则半群上纯整同余的核的一个公开问题,讨论何种情况下纯整同余的核是群带.并给出其同余核上Green关系(H)为同余的一个表示.     

序半群的正则同余类

本文的目的是给出一个序半群的子集能成为某个正则同余的同余类的刻面,同时我们可以容易看出[5]中的关于一般半群(没有序关系)的相应的结论仅是本文的结论的应用.     

The Least Regular Order with Respect to a Regular Congruence on Ordered Γ-Semigroups

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 Γ-semigroups. We can see that any semigroup can be considered as a Γ-semigroup. In this paper, we introduce and characterize the concept of the regular congruences on ordered Γ-semigroups and prove the following statements on an ordered Γ-semigroup M : (1) Every ordered semilattice congruences is a regular congruence. (2) There exists the least regular order on the Γ-semigroup M/ρ with respect to a regular congru- ence ρ on M . (3) The regular congruences are not ordered semilattice congruences in general.     

半群的模糊同余扩张

本文引入半群的模糊同余扩张的概念,给出了模糊同余扩张的同态性质,同时,本文研究了带有模糊同余扩张性质的半群类,证明了一个半群S有模糊同余扩张性质当且仅当S有同余扩张性质,最后进一步给出 有模糊同余张张性质的半群类的特征。     

序半群序同余的一个注记

序半群S的什么子集可以作为S的同余类是一个重要的问题. 在文[8]中,作者证明了如果序半群S的 理想$C$是$S$的某个同余类, 则$C$是凸的; 而且当$C$是强凸理想时，逆命题成立. 在本文中, 我们给出了序半群同余的一个新的构造，并证明了序半群$S$的理想$B$是$S$的某个同余类的充要条件是$B$是凸的.     

Congruences on *-Regular Semigroups

In this paper we study the congruences of *-regular semigroups, involution semigroups in which every element is p-related to a projection (an idempotent fixed by the involution). The class of *-regular semigroups was introduced by Drazin in 1979, as the involutorial counterpart of regular semigroups. In the standard approach to *-regular semigroup congruences, one ,starts with idempotents, i.e. with traces and kernels in the underlying regular semigroup, builds congruences of that semigroup, and filters those congruences which preserve the involution. Our approach, however, is more evenhanded with respect to the fundamental operations of *-regular semigroups. We show that idempotents can be replaced by projections when one passes from regular to *-regular semigroup congruences. Following the trace-kernel balanced view of Pastijn and Petrich, we prove that an appropriate equivalence on the set of projections (the *-trace) and the set of all elements equivalent to projections (the *-kernel) fully suffice to reconstruct an (involution-preserving) congruence of a *-regular semigroup. Also, we obtain some conclusions about the lattice of congruences of a *-regular semigroup. This revised version was published online in June 2006 with corrections to the Cover Date.     

阿基米德序半群的链(英文)

本文通过一个序半群S上的一些二元关系以及它的理想(右理想,双理想)的根集分别给出了该序半群是阿基米德(右阿基米德,t-阿基米德)序子半群的链的刻画.进一步证明了准素序半群是阿基米德序半群的链.最后,通过素根定理证明了序半群S是阿基米德序子半群的链当且仅当S是阿基米德序子半群的半格且S的所有素理想关于集合的包含关系构成链.     

Some Characterizations of Strongly Semisimple Ordered Semigroups

In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup $S$ is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of $S$. In particular, we prove that $S$ is strongly semisimple if and only if each fuzzy left ideal of $S$ is the intersection of all quasi-prime fuzzy left ideals of $S$ containing it.     

阿基米德序半群的链的若干刻画

本文首先引入了一个序半群$S$的准素模糊理想的概念,通过序半群$S$上的一些二元关系以及它的理想的模糊根给出了该序半群是阿基米德序子半群的半格的一些刻画.进一步地借助于序半群$S$的模糊子集对该序半群是阿基米德序子半群的半格进行了刻画.尤其是通过序半群的模糊素根定理证明了序半群$S$是阿基米德序子半群的链当且仅当$S$是阿基米德序子半群的半格且$S$的所有弱完全素模糊理想关于模糊集的包含关系构成链.     

Fuzzy Good Congruences on Left Semiperfect Abundant Semigroups

Motivated by studying fuzzy congruences in groups, semigroups, and ordered semigroups, and as a continuation of N. Kuroki and Y. Tan's works in regular semigroups in terms of fuzzy subsets, in this article we introduce the notions of a fuzzy good congruence relation, a fuzzy cancellative congruence relation on abundant semigroups, and give some properties, and characterizations of fuzzy good congruences on such semigroups. Furthermore, we characterize fuzzy good congruences of left semiperfect abundant semigroups, and get sufficient and necessary conditions for an abundant semigroup to be left semiperfect.