U-纯正半群

型彬半群是正则半群类中纯正半群的一个自然推广．这类半群最先由E1-Qallali和Fountain研究．本文定义了U-纯正半群．这类半群是纯正半群和型W半群二者在U-半富足半群类中的一个共同推广．首先我们确定了U-纯正半群上包含在关系HU中的最小允许同余．借此,证明了半群S为U-纯正半群,当且仅当S可以表示为一个Hall半群和一个V—ample半群的织积．这一结果不仅推广了关于纯正半群结构的著名Hall—Yamada定理,而且推广了E1-Qallali和Fountain建立的型W半群的结构定理．     

半群的区间值反模糊子半群的性质

作为模糊代数的一个研究领域,区间值模糊子半群对模糊子半群的研究至关重要.引入了半群的区间值反模糊子半群的概念,对区间值反模糊子半群的性质进行了研究.讨论了半群的区间值反模糊子半群关于并运算的封闭性质.最后给出了半群的区间值模糊子半群的同态像和原像的相关性质.相关的研究结果丰富了半群的模糊理论.     

素数阶群的约简(共轴)模糊幂半群结构

本文给出了素数阶群上的约简模糊幂半群、共轴模糊幂半群的概念。利用OP-极限讨论了约简模糊幂半群、共轴模糊幂半群中子半群的性质。刻画了约简模糊幂半群、共轴模糊幂半群的结构。     

全正则子半群构成链的正则半群(英文)

本文考虑全正则子半群构成链的正则半群,得到了正则半群具有全正则子半群构成链的一个充分必要条件,这推广了Jones关于具有全正则子半群构成链的逆半群的结果.特别地,建立了具有全正则子半群构成链的完全0-单半群的结构.     

正规Ehresmann型wrpp半群

众所周知,Clifford半群是正则半群类中的一类重要半群,本文定义正规 Ehresmann型wrpp半群,它是Clifford半群在wrpp半群类中的推广,给出了此类半群的若干刻划.     

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.     

正则交半群

进一步研究了正则交半群，引入了纯下在交半群的概念，分别给出了完全正则半群为正则交半群与正交半群的刻划。     

拟纯整半群的构造

作为群的推广,有两类重要的正则半群:完全单半群和逆半群。该两类半群已被分别推广为完全正则半群和纯整半群,并得到了广泛深入的研究。作为后两者的共同推广,本文定义了一类正则半群,称为拟纯整半群。研究了该类半群的若干特征性质,并应用双序集理论给出了它们的结构。     

半群的广义Clifford定理

令U为U-半富足半群的投射元集合.每个H-类含投射元的U-富足半群称为U-超富足半群.这种半群是完全正则半群和超富足半群在U-半富足半群类中的一个共同推广.1941年,Clifford证明了半群S为完全正则半群,当且仅当S为完全单半群的半格.40多年后,Fountain将这一结果推广到了超富足半群上.本文关于U-超富足半群得到了广义Clifford定理.这一结果分别以Clifford和Fountain的上述结果为其推论.     

Γ-半群异于通常半群的独特性质

本文研究了Γ-半群的一些性质.利用研究通常半群的方法,并结合Γ-半群的特殊性,获得了关于Γ-半群性质,推广了通常半群的结论,特别探讨了Γ-半群的夹心集.     

The Structure of NBe—rpp Semigroups

§ 1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　ＡｓｅｍｉｇｒｏｕｐＳｉｓｃａｌｌｅｄａｎｒｐｐｓｅｍｉｇｒｏｕｐｉｆａｌｌｐｒｉｎｃｉｐａｌｒｉｇｈｔｉｄｅａｌｓａＳ1(ａ∈Ｓ)ｏｆＳ ,ｒｅｇａｒｄｅｄａｓａｎＳ1 ｓｙｓｔｅｍ ,ａｒｅｐｒｏｊｅｃｔｉｖｅ (ｓｅｅ,[1 ]ａｎｄ [2 ] ) .ＡｓｅｍｉｇｒｏｕｐＳｉｓａｎｒｐｐｓｅｍｉｇｒｏｕｐｉｆａｎｄｏｎｌｙｉｆｆｏｒａｌｌａ∈Ｓ ,ｔｈｅｓｅｔＭａ ={ｅ∈Ｅ Ｓ1ａ Ｓｅａｎｄ ( ｘ ,ｙ∈Ｓ1)ａｘ=ａｙ ｅｘ=ｅｙ}ｉｓｎｏｎｅｍｐｔｙ ,ｗｈｅｒｅＥ …     

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.     

The construction of orthodox super rpp semigroups

We define orthodox super rpp semigroups and study their semilattice decompositions. Standard representation theorem of orthodox super rpp semigroups whose sub-band of idempotents is in the varieties of bands described by an identity with at most three variables are obtained.     

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.     

Super rpp semigroups

We study a class of special strongly rpp semigroups, namely, the class of super rpp semigroups. These super rpp semigroups are generalizations of both superabundant semigroups and Clifford semigroups within the class of rpp semigroups. In particular, we prove that a super rpp semigroup is a semilattice of D ^(l)-simple strongly rpp semigroups. Our result not only generalizes a well-known theorem of Clifford in the class of completely regular semigroups but also strengthens some structure theorems obtained by Ren-Shum for superabundant semigroups which are orthodox. Some special super rpp semigroups are considered and discussed.     

SOME REMARKS ON （L）-GREEN’S RELATIONS AND STRONGLY RPP SEMIGROUPS

In order to study rpp semigroups, in particular, some special cases, several facts on (l)-Green’s relations and strongly rpp semigroups are given as some remarks.     

On left C-wrpp semigroups

It is known that a C–rpp semigroup can be described as a strong semilattice of left cancellative monoids. In this paper, we introduce the class of left C–wrpp semigroups which includes the class of left C–rpp semigroups as a subclass. We shall particularly show that the semi-spined product of a left regular band and a C–wrpp semigroup forms a curler which is a left C–wrpp semigroup and vice versa. Results obtained by Fountain and Tang on C–rpp semigroups are extended and strengthened.     

On a theorem of c—wrpp semigroups

In this paper, we define a class of semigroups called C—wrpp semigroups and prove that they are a generalization of C—rpp semigroups. Moreover, Theorem 3.1 generalizes immediately the structure theorem for Clifford semigroups [5] and the main result of J. B. Fountain [3].     

Exponential epigroups

We show that an exponential epigroup is a band of unipotent exponential epigroups (in which the set of idempotents forms a subsemigroup). Also, we investigate the structure of unipotent exponential epigroups. In addition, a characterization of the least normal band of groups congruence is given for an arbitrary medial epigroup. It is also shown that k-exponential eventually regular semigroups are necessarily epigroups.