The Closed Subsemigroups of a Clifford Semigroup

In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that {∪α∈Y′ Gα | Y′∈ P(Y) } is the set of all closed subsemigroups of a Clifford semigroup S = [Y; Gα; ?α, β], where Y′denotes the subsemilattice of Y generated by Y′. In particular, G is the only closed subsemigroup of itself for a group G and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring P(S) is isomorphic to the semiring P(Y) for a Clifford semigroup S = [Y; Gα; ?α, β].     

半群M_n的主因子的极大正则子半群

设Sing_n是[n]上的奇异变换半群,得了变换半群M_n={α∈Sing_n:max{|xα~(-1)}≥|im(α)|(x∈im{α))}的主因子的极大正则子半群的完全分类.     

半群OCK_n的理想的极大子半群

设X_n={1,2,…,n}并赋予自然数序,OCK_n是X_n上的具有核连续的保序变换半群.将考虑OCK_n的理想OCK(n,r)={α∈OCK_n:|imα|≤r}(3≤r≤n-1),并得到了OCK(n,r)的极大子半群的完全分类.     

Clifford拟正则半群的半直积

给出了两个半群S和T的半直积是Clifford拟正则半群的充要条件，同时还讨论了S和T^e半直积的结构，其中T^e＝{t^e|Vt∈T,Vc∈E（S）}。     

一类Clifford半群的幂半群

Let S =∪（Gα ： α ∈ E） be a semilattice of groups（i.e., a Cliford semigroup） and n a natural number. E is called an n-element chain of groups if it is an n-element chain. Denote by Cn the set of all n-element chains of groups. In this paper we shall show that for any natural number n, the class of semigroups Cn satisfies the strong isomorphism property.     

PO_n的局部极大幂等元生成的子半群

研究了有限链上的部分保序变换半群PO_n.通过对其幂等元的分析,获得了PO_n的局部极大幂等元生成的子半群的结构与分类.     

Characterizations of Clifford semigroup digraphs

This paper characterizes directed graphs which are Cayley graphs of strong semilattices of groups and, in particular, strong chains of groups, i.e. of completely regular semigroups which are also called Clifford semigroups.     

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.     

全子半群构成链的富足半群

全子半群定义为含有所有幂等元的子半群.半群称为▽_(fs)-半群,如果它的所有全子半群关于集合包含关系构成一个链.本文研究富足▽_(fs)-半群,得到这类半群的若干特征,特别地,建立了完全0-单▽_(fs)-半群和满足正则性条件的本原富足▽_(fs)-半群的结构.     

On a Class of Subdirect Products of Left and Right Clifford Semigroups

Abstract

Regular semigroups S with the property eS ? Se or Se ? eS for all idempotents e ∈ S include all left and right Clifford semigroups. Characterizations of such semigroups are given and their structure investigated, in particular in terms of spined products of left and right Clifford semigroups with respect to Clifford semigroups.     

The Semigroup Structure of Left Clifford Semirings

In this paper,we generalize Clifford semirings to left Clifford semirings by means of the so-called band semirings.We also discuss a special case of this kind of semirings,that is, strong distributive lattices of left rings.     

含幺Clifford半群上的Rees矩阵半群的同余和正规加密群结构

给出了含幺Clifford半群上的Rees矩阵半群S的正规加密群结构,证明了在含幺Clifford半群上的Rees矩阵半群S上以下两个条件是等价的:(1)S上的同余ρ是完全单半群同余;(2)S上的同余ρ和S上的相容组之间存在保序双射.最后还证明了S上的完全单半群同余所构成的同余格是半模的.     

两个模糊子半群集合之间的同态

设S,T是半群,F(S)和F_s(S)分别表示S的所有模糊子集的集合和所有模糊子半群的集合。文中,讨论了F(S)(F_s(S))和F(T)(F_s(T))之间的模糊同态,建立了模糊商子半群的概念,把分明半群的基本同态定理推广到模糊子半群。     

Inverse Subsemigroups of the Monogenic Free Inverse Semigroup

It is shown that every finitely generated inverse subsemigroup (submonoid) of the monogenic free inverse semigroup (monoid) is finitely presented. As a consequence, the homomorphism and the isomorphism problems for the monogenic free inverse semigroup (monoid) are proven to be decidable.     

一类Clifford半群的刻画

G是一个群,I是一个指标集.令CG=G×I={(g,i):g∈G,i∈I};(a,i)(b,j)=(ab,k)with k=min{i,j}则CG是一个半群.事实上,CG是Clifford半群,并且CG代表了一类特殊的Clifford半群.     

Various notions of weak injectivity over Clifford semigroups

We study various notions of weak injectivity of acts over a Clifford semigroup. In addition we characterize weak self-injectivities of several classes of Clifford semigroups constructed via particular kinds of groups and group homomorphisms. Research of X. Zhang supported by the China Scholarship Council No. 2006101056. Research of Y. Wang supported by National Natural Science Foundation of China Research Grant 10571181.     

幺半群的强半格上的Rees矩阵半群的平移壳

设含幺元的半群A是幺半群A~_e的半格,其中A的幺元为1_A,A~_e的幺元为e,所有幺元e的集合为E(A),则对于幺半群A上的Rees矩阵半群S和幺半群A~_e上的Rees矩阵半群S~_e,以下五个条件是等价的:(1)任意的e∈E(A),a∈A,有ae=ea;(2)A是幺半群A~_e的强半格;(3)S是S~_e的强半格;(4)A的平移壳和A~_e的平移壳的强半格同构;(5)S的平移壳和S~_e的平移壳的强半格同构.     

全变换半群的极大逆子半群的两个注记

设Tn是集合Xn={1．2，…．n}上的全变换半群．本文证明了Tn的每个极大逆子半群有群核。我们从一个群H一类和Tn的两类子半格，构造出两类新的Tn的极大逆子半群．其结果部分回答了Schein提出的特征Tn的极大逆子半群的公开问题．     

半格序Clifford半群

证明了每一个半格序Clifford半群都能嵌入到其加法半群的半格序自同态半群当中;给出了同余单的半格序Clifford半群所具有的几种形式,得到了自然半格序零群是仅有的次直不可约自然半格序Clifford半群.     

矩阵逆半群

讨论矩阵逆半群的一些基本性质, 证明矩阵逆半群的幂等元集是有限布尔格的子半格, 从而证明等秩矩阵逆半群是群, 然后完全确定二级矩阵逆半群的结构：一个二级矩阵逆半群或者同构于二级线性群,或者同构于二级线性群添加一个零元素,或者是交换线性群的有限半格, 或者满足其他一些性质; 对于由某些二级矩阵构成的集合, 我们给出了它们成为矩阵逆半群的充分必要条件.