0-范畴,强〈E〉*-稠密半群

我们通过本原逆半群作用在强〈E〉-酉,〈E〉-稠密范畴上,给出了0-范畴,(强)〈E〉*-稠密,强〈E〉*-酉半群的一个刻画.我们也证明了每一个0-范畴,强〈E〉*-稠密半群有一个0-范畴,(强)〈E〉*-稠密,强〈E〉*-酉的覆盖.     

0-范畴E-酉逆半群的结构

本证明了每一个0-范畴E-酉逆半群能被嵌入到半格与本原逆半群的λ一半直积中。     

*-双单型A半群(英文)

一个逆半群如果只有一个D-类,则称为双单逆半群.一个型A半群只有一个D*-类和一个正则D-类,则称为*-双单型A半群.本文采用McAlister的刻画双单逆半群的方法([Proc.London Math.Soc.,1974,28(2):193-221]),用一致半格和可消幺半群建立了*-双单型A半群的结构.     

C-半群与C_0—半群的关系

在这篇文章中证明了C-半群在限制空间中为C_0-半群,首次讨论了C-半群的解析性     

具有左单S-恰当断面的富足半群的结构(英文)

本文得到具有左单恰当断面的富足半群的进一步刻画.推广并丰富了Blyth和AlmeidaSantos于1996年得到的关于左单逆断面及两位作者分别于2008年与2010年得到的关于恰当断面的相关结果.建立了具有左单S-恰当断面的富足半群的结构.     

C0-半群拓扑(Ⅰ)

利用有界线性算子半群,引入了一新的局部凸向量拓扑,并对其基本性质进行了讨论.     

C_0-半群拓扑(I)

利用有界线性算子半群,引入了一新的局部凸向量拓扑,并对其基本性质进行了讨论.     

类型μ恰当半群的结构(英文)

本文的目的是用可消幺半群的强半格和基本恰当半群建立一类恰当半群的结构.首先,引入了类型μ恰当半群,然后构造了一类代数,Y-积.证明了每个Y-积是类型μ恰当半群;反之,每个类型μ恰当半群同构于一个Y-积.     

Banach空间上强混合的C0-半群

证明了每个可分无限维复Banach空间上都存在一个强混合的Co-半群,在加权函数空间上给出了转移半群是强混合的一个充要条件.     

具有CO-恰当断面富足半群的一种构造方法

本文首先研究了具有可消模断面的拟恰当半群的结构,然后给出了用可消模断面的拟恰当半群构造具有CO-恰当断面富足半群的方法.     

0-对偶预同态的一个充要条件

我们对带零逆半群定义了0-对偶预同态的概念,给出并证明了0-对偶预同态的一个等价条件.     

Semitransitive subsemigroups of the symmetric inverse semigroups

We initiate the study of semitransitive transformation semigroups. In the paper we describe the structure of semitransitive subsemigroups of the finite symmetric inverse semigroup of the minimal cardinality modulo the classification of transitive subgroups of the minimal cardinality of finite symmetric groups, and state the results on minimal transitive subsemigroups. The authors were supported in part by Ukrainian-Slovenian bilateral research grants from the Ministry of Education and Science, Ukraine, and the Research Agency of the Republic of Slovenia.     

On 0-homology of categorical at zero semigroups

The isomorphism of 0-homology groups of a categorical at zero semigroup and homology groups of its 0-reflector is proved. Some applications of 0-homology to Eilenberg-MacLane homology of semigroups are given.      

一类无穷维Hamilton算子的半群生成定理

研究了无穷维H am ilton算子生成C0半群的问题,得到了类无穷维H am ilton算子生成C0半群的一个充分条件.把结果应用在一类双曲型混合问题生成的无穷维H am ilton算子上,证明此类算子生成C0半群,并利用H ille-Y osida定理进一步说明了结果的正确性和有效性.另外,还给出了波动方程相应的无穷维H am ilton算子所生成的C0半群的具体表达式.     

Associate inverse subsemigroups of regular semigroups

By an associate inverse subsemigroup of a regular semigroup S we mean a subsemigroup T of S containing a least associate of each x∈S, in relation to the natural partial order ≤ _S . We describe the structure of a regular semigroup with an associate inverse subsemigroup, satisfying two natural conditions. As a particular application, we obtain the structure of regular semigroups with an associate subgroup with medial identity element. Research supported by the Portuguese Foundation for Science and Technology (FCT) through the research program POCTI.     

具有左简纯正断面的正则半群

本文引入并研究了左简纯正断面, 得到了与之相关的若干刻画; 推广并丰富了Blyth 和AlmeidaSantos 于1996 年得到的关于左简逆断面及Kong 于2007 年得到的关于纯正断面的相关结果; 同时,给出了具有左简纯正断面的正则半群的结构定理.     

Cayley color graphs of inverse semigroups and groupoids

The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.     

Frucht theorem for inverse semigroups

In the paper, the problem of representing a finite inverse semigroup by partial transformations of a graph is treated. The notions of weighted graph and its weighted partial isomorphisms are introduced. The main result is that any finite inverse semigroup is isomorphic to the semigroup of weighted partial isomorphisms of a weighted graph. This assertion is a natural generalization of the Frucht theorem for groups. Translated fromMatematicheskie Zametki, Vol. 61, No. 2, pp. 246–251, February, 1997. This research was partially supported by the International Science Foundation under grant No. GSU 041049. Translated by A. I. Shtern     

Semigroup closures of finite rank symmetric inverse semigroups

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations I _λ ⁿ of the rank ≤ n is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. We also derive related results about the nonexistence of (partial) compactifications of classes of semigroups that we consider.