L—逆左系对幺半群的刻画

正则左Ｓ－系是ｖｏｎ ｎｅｕｍａｎｎ正则半群的自然推广，逆左Ｓ－系是逆半群的自然扩广，作为左逆半群的自然推广，本文引入了Ｌ－逆左系的概念，并用来刻画了几类幺半群，如左逆幺半群，逆幺半群，ａｄｅｑｕａｔｅ幺半群等。     

右（左）逆半群的半直积及圈积

给出了两个幺半群的半直积及圈积为右（左）逆半群的充分必要条件，从而推广了[2]中两个幺半群的半幺直积和圈积为逆半群的充分必要条件．     

关于左完全幺半群

设Ｓ是左完全幺半群．本文讨论了左，右Ｓ－系的链条件，特别地证明了右Ｓ－系的Ｂｊｏｒｋ定理．     

关于所有强平坦右S-系是正则系的幺半群(英)

本论文考虑了所有强平坦右S-系是正则系的幺半群的刻画,证明了所有强平坦右S-系是正则S-系当且仅当S是右PSF幺半群并且S的每一个左coilpasible子幺半群包含左零元．该结果对Kilp和Knauer在文献[7]中的问题给出了一个新的回答．     

右消去幺半群、左正则带和左正则型A幺半群

本文利用右消去幺半群,左正则带建立了真左正则型A幺半群．在证明了任一左正则型A幺半群均有P－覆盖后,给出P－覆盖的结构．     

L*-逆半群的结构

定义了L*-逆半群,并引入了半群左圈积的概念.证明了半群S是一个L*-逆半群,当且仅当S是一个型A半群Γ和一个左正则带B连同结构映射ψ的左圈积B( )ψΓ.这一结果的一个直接推论是关于左逆半群结构的著名Yamada定理.利用半群的左圈积,给出了一个非平凡的L*-逆半群的例子.     

П正则半群的幂等元同余类

本文分别给出П正则半群的幂等元同余类和Пｏｒｔｈｏｄｏｘ半群［１］的幂等元同余类的П正则性刻画．其次，证明П逆半群或完全П正则半群Ｓ的幂等元同余类是Ｓ的П正则子半群．最后讨论ｏｒｔｈｏｄｏｘ半群的幂等元同合类的正则性．     

具有中心幂等元的L-弱正则半群

本文定义了具有中心幂等元的(L)-弱正则半群,研究了这类半群的代数结构.利用半群上的右同余(L)+和左同余R+,证明了半群S是一个具有中心幂等元的(L)-弱正则半群,当且仅当S是H-左可消幺半群的强半格.这推广了Clifford半群的相应结果.     

图的强收缩核与图的强自同态幺半群的正则性

本文研究图及其强自同态幺半群．首先刻画了图的强自同态幺半群的正则元，然后给出了此幺半群正则的充要条件．这推广了［１］和［２］中关于有限图的强自同态幺半群正则的结果．     

正规纯正左消幺半群并半群上的(*,~)-好同余(英文)

本文利用(*,~)-好同余对刻画了正规纯正左消幺半群并半群上的(*,~)-好同余.此结果将正则半群中有关正规纯正群并半群上同余的相关结论推广到了r-wide半群中.     

The structure of L*-inverse semigroups

The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.     

The structure of ?*-inverse semigroups

The concepts of ℒ*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the ℒ*-inverse semigroup can be described as the left wreath product of a type A semigroup Γ and a left regular band B together with a mapping which maps the semigroup Γ into the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the ℒ*-inverse semigroups by using the left wreath products.     

Abundant Left C-lpp Proper Semigroups

The aim of this paper is to study a class of left abundant semigroups, so-called abundant left C-lpp proper semigroups including left type A proper semigroups and right inverse proper semigroups as its subclasses. A structure theorem similar to McAlisters for inverse proper semigroups is obtained. As its application, it is verified that any abundant left C-lpp proper semigroup can be embedded into a semidirect product of a left regular band by a cancellative monoid.AMS Subject Classification (1991): 20M10Suppoted by the Foundation of Yunnan University and also by the Director Foundation of Yunnan Province.     

左C-wrpp 半群的左$\Delta$-积

We study another structure of so-called left C-wrpp semigroups. In particular, the concept of left △-product is extended and enriched. The aim of this paper is to give a construction of left C-wrpp semigroups by a left regular band and a strong semilattice of left-R cancellative monoids. Properties of left C-wrpp semigroups endowed with left △-products are particularly investigated.     

Characterization of Inverse and Left Inverse SemigroupsbyTheirS1┐acts

ＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＩｎｖｅｒｓｅａｎｄＬｅｆｔＩｎｖｅｒｓｅＳｅｍｉｇｒｏｕｐｓｂｙＴｈｅｉｒＳ１┐ａｃｔｓ＊）ＬｉｕＺｈｏｎｇｋｕｉ（刘仲奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｗｅｓｔＮｏｒｍａｌＵｎｉｖ...     

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.     

On Left Regular Ordered Semigroups

The main result of the paper is a decomposition theorem of the left regular ordered semigroups into left regular and left simple semigroups.     

Naturally ordered regular semigroups with an inverse monoid transversal

The notion of an inverse transversal of a regular semigroup is well-known. Here we investigate naturally ordered regular semigroups that have an inverse transversal. Such semigroups are necessarily locally inverse and the inverse transversal is a quasi-ideal. After considering various general properties that relate the imposed order to the natural order, we highlight the situation in which the inverse transversal is a monoid. The regularity of Green’s relations is also characterised. Finally, we determine the structure of a naturally ordered regular semigroup with an inverse monoid transversal.     

左C-半群的左交错积结构

给出了左C-半群的另一种结构,所谓左交错积结构,并刻画了它的特殊情形.这种结构为左C-半群在广义正则半群类中的再推广奠定了基础.     

Embedding Into Almost Left Factorizable Restriction Semigroups

The notion of almost left factorizability and the results on almost left factorizable weakly ample semigroups, due to Gomes and the author, are adapted for restriction semigroups. The main result of the paper is that each restriction semigroup is embeddable into an almost left factorizable restriction semigroup. This generalizes a fundamental result of the structure theory of inverse semigroups.