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.     

正则半群的左Clifford同余

本文给出了左 Clifford 半群的一个等价条件,研究了正则半群上的左 Clifford同余,用同余的核和同余的超迹描述了左 Clifford 同余,右 Clifford 同余和 Clifford 同余。     

关于rpp半群的fuzzy同余注记

半群S称为rpp半群,若它的所有L~*类都含幂等元.rpp半群S称为C-rpp半群,若它的幂等元集含于S的中心.这里利用半群上fuzzy同余的概念,引入了rpp半群上fuzzy左好同余的定义并得到了它的一些性质,给出了此类半群的刻画,并对具有某种特性的rpp半群(如强rpp半群和完备rpp)作了讨论.最后,得到了一类rpp半群为完备rpp半群的充要条件.以上结论是对Fountain关于rpp半群研究结果的推广和补充.     

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.     

完备右拟富足半群

在强E-右拟富足半群上定义关系γ,得到γ的性质.利用关系γ,主要研究了一类拟富足半群一完备右拟富足半群,得出这类半群的结构定理.另外,给出这类半群的另一种刻画.     

富足半群上的fuzzy-t同余

引入富足半群上fuzzy-t同余的概念,给出富足半群上fuzzy-t同余的性质和特征。在此基础上,给出满足正则性条件的富足半群上fuzzy-t同余的性质。最后,就若干特例作讨论,得到一些结果。     

弱左ample半群上的fuzzy幂单同余

引入了左半富足半群上fuzzy强同余的概念,给出了左半富足半群上fuzzy强同余的性质和特征。在此基础上,给出了弱左ample半群上fuzzy强同余和fuzzy幂单同余的性质,得到了弱左ample半群上的fuzzy强同余为fuzzy幂单同余的充要条件。     

左富足半群上的同余（英文）

本文研究了一类特殊的左富足半群,即左GC-lpp-半群上的R^*-同余.我们利用类似正则半群上同余的核迹方法分别刻画了这类半群上具有相同核和迹的最大和最小同余.同时,我们也得到了左GC-lpp-半群上的幂等元R*-同余的一些性质,并建立了这种同余的结构.     

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。     

基于弱型B半群上的fuzzy同余的几点注记

利用fuzzy关系的概念给出了半富足半群上fuzzy强同余的定义,得到了半富足半群上fuzzy强同余的性质和特征。在此基础上,给出了弱型B半群上fuzzy强同余和fuzzy幂单同余的性质,证明了弱型B半群上的fuzzy强同余为fuzzy幂单同余的充要条件。     

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.     

关于Fuzzy完全正则半群

本文先引入Ｆｕｚｚｙ左（Ｆｕｚｚｙ右）正则半群的概念，进而讨论Ｆｕｚｚｙ左（Ｆｕｚｚｙ右）正则半群以及Ｆｕｚｚｙ完全正则半群中Ｆｕｚｚｙ理想的一些代数性质。     

Some Characterizations of Left Weakly Regular Ordered Semigroups

In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (generalized) bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.     

关于序半群的模糊拟理想

In this paper,fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets.Furthermore,we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals.Finally,we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.     

纯正半群上的同余扩张(一)

刻划半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题．本文讨论了带上的同余的正规性和不变性以及在其Ｈａｌｌ半群上的扩张，从同余扩张的角度刻划了带上的同余的性质，给出了扩张的极大、极小同余的描述．     

Some relations on completely regular semigroups

A semigroup S is called a Clifford semigroup if it is completely regular and inverse. In this paper, some relations related to the least Clifford semigroup congruences on completely regular semigroups are characterized. We give the relation between Y and ξ on completely regular semigroups and get that Y ^* is contained in the least Clifford congruence on completely regular semigroups generally. Further, we consider the relation Y ^*, Y, ν and ε on completely simple semigroups and completely regular semigroups. This work is supported by Leading Academic Discipline Project of Shanghai Normal University, Project Number: DZL803 and General Scientific Research Project of Shanghai Normal University, No. SK200707.     

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.     

Tight inverse semigroups that are not bisimple

A semigroup is tight if each of its congruences is uniquely determined by each of the congruence classes. Bisimple inverse semigroups are tight, and tight semigroups are either simple or congruence-free with zero. Although congruence-free semigroups are tight, they are not necessarily bisimple. We construct tight inverse semigroups and tight inverse monoids that are neither bisimple nor congruence-free.