具有逆断面的正则半群的同余的表示

具有道断面S°的正则半群可表示为有Saito's结构的半群W（I，S°，Λ，*，α，β）.我们利用由I，S°和Λ上的同余构成的所谓同余聚抽象地表示这类半群上的同余，进而给出了这类半群的同态象的构造法．     

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．     

关于具有$Q$-逆断面的正则半群的同余格

In this paper, a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed. The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly.     

D—正则半群上的同余

刻划Ｄ－正则半群上的如下同余：包括在Ｄ［Ｒ］中的最大同余、最大幂等元分离同余、（最小）基本强Ｄ－同余和群同余。     

-正则半群上的同余

刻划-正则半群上的如下同余:包括在中的最大同余、最大幂等元分离同余、(最小)基本强-同余和群同余。     

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。     

正则半群上的广义逆半群同余

利用同余的核与超迹描述正则半群上的广义逆半群同余。     

完全零单半群的模糊同余

介绍完全零单半群上的真模糊同余和连接模糊三元组的概念,由此得到完全零单半群上的真模糊同余集和连接模糊三元组集之间的双射。     

强P-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.     

(P)-反演半群上的模糊强(P)-同余

给出模糊强(P)-同余的概念,接着用"弱(P)-逆"研究-反演半群S(P)上的强-同余,最后借助于由P上的模糊正规等价关系ξ及S(P)上的模糊正规子集K组成的模糊强(P)-同余对(ξ-K)刻画(P)-反演半群S(P))上的模糊强(P)-同余.     

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.     

完全单半群及完全正则半群的逆断面

指出完全单半群Ｓ的任何一个Ｆ－类是逆断面,且为Ｑ－逆断面,而Ｓ的任何一个逆断面必是一个Ｆ－类,因而所有逆断面同构。并且给出完全正则半群的逆断面存在的充要条件。     

Regular Semigroups with Inverse Transversals

Let C be a semiband with an inverse transversal . In [7], G.T. Song and F.L. Zhu construct a fundamental regular semigroup with an inverse transversal . is isomorphic to a subsemigroup of the Hall semigroup of C but it is easier to handle. Its elements are partial transformations, and the operation-although not the usual composition-is defined by means of composition. Any full regular subsemigroup T of is a fundamental regular semigroup with inverse transversal . Moreover, any regular semigroup S with an inverse transversal is proved to be an idempotent-separating coextension of a full regular subsemigroup T of some . By means of a full regular subsemigroup T of some and by means of an inverse semigroup K satisfying some conditions, in this paper, we construct a regular semigroup with inverse transversal such that is isomorphic to K and to T. Furthermore, it is proved that if S is a regular semigroup with an inverse transversal then S can be constructed from the corresponding T and from in this way.     

关于Clifford半群上的fuzzy同余

利用半群fuzzy同余的概念,讨论一类特殊的完全正则半群,即Clifford半群上的fuzzy同余.研究该类半群上fuzzy同余的性质.在此基础上,给出Clifford半群上fuzzy同余的性质和特征,得到Cllifford半群上fuzzy同余为fuzzy消去同余的充要条件.     

Fundamental Regular Semigroups with Inverse Transversals

Abstract. Let C be a regular semigroup with an inverse transversal C° and let C be generated by its idempotents. Following W. D. Munn and T. E. Hall's idea, in this paper, a fundamental regular semigroup T _C,C° with an inverse transversal T _C,C° ° is constructed such that the following holds. For any regular semigroup S with an inverse transversal S° and < E(S)>=C , C°=C∩ S° , there is a homomorphism φ from S to T _C,C° such that the kernel of φ is the maximum idempotent-separating congruence on S , and φ satisfies: (1) φ| _C is a homomorphism from C onto < E(T _C,C° )> ; (2) φ| _S° is a homomorphism from S° to T _C,C° ° . In particular, S is fundamental if and only if S is isomorphic to a full subsemigroup of T _C,C° . Our fundamental regular semigroup T _C,C° is isomorphic to a subsemigroup of the Hall semigroup of C but it is easier to handle. Its elements are partial transformations, and the operation—although not the usual composition—is defined by means of composition.     

正则纯整群带的算子半群和同余网

正则半群Ｓ的同余格（Ｓ）上的算子Ｋ，ｋ，Ｔ和ｔ定义如下：对于ρ∈Ｓ，ρＫ和ρｋ（ρＴ和ρｔ）分别是与ρ有相同核（迹）的最大和最小同余．我们确定了所有正则纯整群带的同余格上由Ｋ，ｋ，Ｔ和ｔ生成的算子半群．并确定了正则纯整群带上任意同余的同余网．