A CLASS OF NATURALLY ORDERED ABUNDANT SEMIGROUPS WITH A GREATESTIDEMPOTENT

On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].

On Abundant Semigroups with Quasi-ideal Adequate Transversals

In this paper, we discuss some properties about an abundant semigroup with a quasi-ideal adequate transversal. Moreover, we show that the product of two quasi-ideal adequate transversals of an abundant semigroup which satisfies some conditions is a quasiideal adequate transversal.

RP-framed富足半群

主要定义了RP-framed富足半群。给出了富足半群S是RP-framed等价于S同构于Rees雷斯矩阵半群M(T;I,Λ;P),其中T是富足幺半群,矩阵P的元都是T的单位群。

保持等价关系的变换半群的一些结果

给出了保持等价关系的变换半群上的格林关系L,R,H和格林*-关系L^(*),R^(*),H^(*)相容的充要条件,刻画了这类半群的左(右,完全)正则性,得到了这类半群的全体幂等元(正则元,富足元)构成子半群的等价描述.

带有左正则带的IC拟适当半群研究

文章利用富足半群上的L^(*)和R^(*)关系,得到了带有左正则带的IC拟适当半群的若干性质,特别是研究了幂等元导出的一类自同态映射。构造了半群上的一类好同余,将商半群简化为型-A半群,组建了一种具有半直积结构的AGC-系统,以此给出了带有左正则带的IC拟适当半群的一般刻画,改进了现有文献的部分结果。

某些Foutain半群上的同余

称幺半群T上的Rees矩阵半群M=M(T;I,Λ;P)为紧的,如果P中的元素来自T中的单位群H.研究了幺半群T的性质与紧Rees矩阵半群M=M(T;I,Λ;P)之间的关系,证明了一个紧的Rees矩阵半群M=M(T;I,Λ;P)同构于一个正规的紧Rees矩阵半群M=M(T;I,Λ;Q),且得到了弱超富足半群T上紧Rees矩阵半群(~)-好同余的一些性质.

有限递减变换半群的商半群的一个注记

令Sing n为X n={1,2,…,n}上的奇异变换半群,令S-n={α∈Sing n|xα≤x,x∈X n},这里1<2<…<n.本文得到富足半群S-n的一类同余ρ,其商半群S-n/ρ非正则且既不左富足也不右富足.

A Class of Left E-adequate Semigroups

In this paper we establish a construction of a class of left E-adequate semigroups by using semilattices of cancellative monoids and fundamental left E-adequate semigroups. We first introduce concepts of type μ^＋（μ^＊,μ ） abundant semigroups and type μ^＋left E-adequate semigroups. In fact, regular semigroups are type μ^＋abundant semigroups and inverse semigroups are type μ^＋left E-adequate semigroups. Next, we construct a special kind of algebras called E^＋-product. It is proved that every E^＋-product is a type μ^＋left E-adequate semigroup, and every type μ^＋left E-adequate semigroup is isomorphic to an E^＋-product of a semilattice of cancellative monoids with a fundamental left E-adequate semigroup. Finally, as a corollary of the main result, it is deduced that every inverse semigroup is isomorphic to an E^＋-product of a Clifford semigroup by a fundamental inverse semigroup.

Factorisable Quasi-adequate Semigroups

In this paper,we investigate a class of factorisable IC quasi-adequate semigroups,so-called,factorisable IC quasi-adequate semigroups of type-（H,I）.Some characterizations of factorisable IC quasi-adequate semigroups of type-（H,I） are obtained.In particular,we prove that any IC quasi-adequate semigroup has a factorisable IC quasi-adequate subsemigroups of type-（H,I） and a band of cancellative monoids.

Abundant Semigroups with a Multiplicative Adequate Transversal

The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal.Some properties and characterizations for such semigroups are obtained.In particular. we establish the structure of this class of abundant semigroups in terms of left normal bands,right normal braids and adequate semigroups with some simple Compatibility conditions.Finally.we apply this structure to some special cases.

半群PO_(n)(k)的格林(星)关系及富足性

设P_(n)和PO_(n)分别是有限链[n]上的部分变换半群和保序部分变换半群.对任意1≤k≤n,令PO_(n)(k)={α∈PO_(n)(k):■x∈dom(α),x≤k■xα≤k},则PO_(n)(k)是P_(n)的子半群.通过分析半群PO_(n)(k)中的元素,获得了半群PO_(n)(k)的格林关系和格林星关系.进一步讨论了:当1≤k≤n-1时,半群PO_(n)(k)是非正则富足半群.

半群O_(n)^([l,m])的格林(星)关系及富足性

设O_(n)是有限链X_(n)上的保序变换半群,对任意1≤l≤m≤n,令O_(n)^([l,m])={α∈O_(n):∀x∈X_(n),l≤xα≤m},易证半群O_(n)^([l,m])是O_(n)的子半群,刻画了半群O_(n)^([l,m])的格林关系和正则元的特征,进一步获得了半群O_(n)^([l,m])的星格林关系及非正则富足性.

Abundant Semigroups with a Quasi-ideal Quasi-adequate Transversal

Characterization theorems for abundant sernigroups having a quasi-ideal quasi-adequate transversal are obtained. Our results generalize and amplify the related results of Satio on regular semigroup obtained in 1985 and Kong obtained in 2007 respectively. Some recent results on this topic given by Guo-Shum are strengthened. In particular, the structure of such an abundant semigroup is described.

Structure of Strict Abundant Semigroups

We introduce a new class of semigroups called strict abundant semigroups,which are concordant semigroups and subdirect products of completely-J*-simple abundant semigroups and completely-J*-simple primitive abundant semigroups.A general construction and a tree structure of such semigroups are established.Consequently,the corresponding structure theorems for strict regular semigroups given by Auinger in 1992 and by Grillet in 1995 are generalized and extended.Finally,an example of strict abundant semigroups is also given.

A Method of Construction for Abundant Semigroups with a CO-Adequate Transversal

In this paper, we first study the structure of quasi-adequate semigroups with a cancellative monoid transversal. By using the above result, we present a method of construction for the abundant semigroups containing a CO-adequate transversal.

保持双向等价关系的变换半群的若干结果

设X为任意集合,E是X上的一个等价关系.TX表示X上的全变换半群.令TE*(X)={f∈TX:对任意x,y∈X,(x,y)∈E当且仅当(f(x),f(y))∈E},则TE*(X)是TX的一个子半群.文章研究了TE*(X)是富足半群的条件,并描述了使得在半群TE*(X)中有D=J的X上的等价关系E.

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。

一类富足半群的结构

利用左正则带和L*-幂单半群,给出了具有S-恰当断面的富足半群的一个结构定理.

型A半群上的fuzzy好同余

引入了富足半群上fuzzy好同余和fuzzy消去同余的概念,给出了富足半群上fuzzy好同余的性质和特征。在此基础上,给出了型A半群上fuzzy好同余的性质。得到了型A半群上的fuzzy好同余为fuzzy消去同余的充要条件。

关于左型A半群上的fuzzy同余

引入了左富足半群上fuzzy右好同余和fuzzy右消去同余的概念,给出了左富足半群上fuzzy右好同余的性质和特征.在此基础上,给出了左型A半群上fuzzy右好同余和fuzzy右消去同余的性质.得到了左型A半群上的fuzzy右好同余为fuzzy右消去同余的充要条件.