关于弱交换PO—半群

在本文中我们引入弱交换ＰＯ－半群的概念，并研究这类半群到其Ａｒｃｈｉｍｅｄｅｓ子半群的半格分解，给出这类半群似于无序半群的相应结果的一个刻画。作为推论，我们得到弱交换ＰＯｅ－群和无序半群的相应刻画。     

弱交换富足序半群(Ⅰ)

本文将序半群上的 Ｇｒｅｅｎ’ｓ－关系推广为 Ｇｒｅｅｎ’ｓ＊一关系．给出主序（左、右）＊－理想、主序＊－滤特征描述和弱交换富足序半群的特征．用这些特征证明了一类弱交换富足序半群的结构定理：若序半群Ｓ满足 ,则Ｓ是弱交换富足序半群当且仅当Ｓ是左（右）单序半群｛（ｅ）（Ｓ）｝的半格．     

2—弱幂P（Δ）—半群

本文刻划了半格不可分的２－弱幂ρ－半群，描述了半格可分的２－弱幂ρ－半群的结构，在此基础上，刻划了２－弱幂Δ－半群。     

几类亚交换序半群

本文研究几类亚交换序半群的性质,并将具有单位元的亚交换序半群的一些结果扩张到这几类亚交换序半群上,使得这些结果更加细化,其中主要证明了以下定理：伪交换序半群可以分解成阿基米德序半群的半格．并且,一般来说,这种分解不是唯一的．     

关于交换序半群的一个注记

给出了正则交换序半群的与素理想结构有关的若干性质，还给出了为有限个主理想的并的交换序半群类中的诺特性，阿基米德性，正则性以及有限生成性之间的一些关系。     

2-弱幂P(△)-半群

本文刻划了半格不可分的＞－弱幂ｐ－半群，描述了半格可分的２－弱幂ｐ－半群的结构．在此基础上，刻划了２－弱幂△－半群．     

弱可约序半群的理想扩张

NioviKehayopulu和Michael Tsingelis于2003年给出了关于序半群的理想扩张的一个定理,本文利用该定理进一步给出了弱可约序半群的理想扩张的构造．     

基本的弱正则*-半群的结构

本文给出了基本的弱正则＊－半群的一个结构定理．作为这一结构定理的特 殊情形，基本的正则＊－半群的一个新的结构被给出．     

交换半群环的分式环

设含幺交换环Ｒ对其乘法子集Ｔ的分式环为ＲＴ，交换幺半群Ｓ在其子半群∑处局部化为Ｓ∑本文证明了Ｒ［Ｓ］对于Ａ的分环式环Ｒ［Ｓ］ＡＭ 构于半群环ＲＴ［Ｓ∑］。     

基半群为O—J—严格单半群的零直并的代数

设Ａ是代数闭域Ｋ上的一个具乘基Ｂ的有限维含幺结合代数，称半群Ｂ∪（０）为Ａ的基半群。本文给出了０－Ｊ－严格单半群的定义，对于基半群为Ｏ－Ｊ－严格单半群的零直并的代数，完全研究了它的代数表示型。     

关于弱交换po－半群

在本文中我们引入弱交换ｐｏ－半群的概念，并研究这类半群到其Ａｒｃｈｉｍｅｄｅｓ子半群的半格分解，给出了这类半群类似于无序半群相应结果的一个刻画。作为推论，我们得到弱交换ｐｏｅ－群和无序半群的相应刻画。     

Quadratic double centralizers and quadratic multipliers

In this paper, we establish stability of quadratic double centralizers and quadratic multipliers on Banach algebras. We also prove the super stability of quadratic double centralizers on Banach algebras which are weakly commutative and weakly without order, and of quadratic multipliers on Banach algebras which are weakly without order.     

交换半群的强半格

本文刻划交换半群的强半格上的最小半格同余，并证明由此得到的商半群为对应的每个交换半群的商半群的强半格。     

Computing finite commutative semigroups: Part II

New precedence results are obtained for semigroups with zero, which describe the first non-zero row in detail and provide effective comparisons with subsequent rows. These results are used to further sharpen existing algorithms for the computation of finite commutative semigroups, confirm the number of distinct commutative semigroups of order 9, and determine the number of distinct commutative semigroups of order 10.     

The structure of commutative semigroups with the ideal extension property

In this paper, we will characterize commutative semigroups which have the ideal extension property (IEP). This characterization describes the multiplicative structure of commutative semigroups with IEP. Establishing this characterization was motivated not only by an interest in IEP itself, but also by the fact that in the category of commutative semigroups, the congruence extension property (CEP) implies IEP. A few preliminary results which hold in the general (non-commutative) case are discussed below. Following these initial observations, all semigroups considered are commutative.     

Commutative semigroups whose homomorphic images in groups are groups

In this paper we study commutative semigroups whose every homomorphic image in a group is a group. We find that for a commutative semigroup S, this property is equivalent to S being a union of subsemigroups each of which either has a kernel or else is isomorphic to one of a sequence T₀, T₁, T₂, ... of explicitly given, countably infinite semigroups without idempotents. Moreover, if S is also finitely generated then this property is equivalent to S having a kernel.     

Semigroups of order 8

We construct all non-equivalent semigroups of order 8, obtain their total number, and specify commutative semigroups, regular semigroups and inverse semigroups among them. And we present their classification with respect to the equivalences of the Green’s relations, that is, egg-box types with information about the positions of idempotent elements in them.     

Computing finite commutative semigroups

Precedence results are used to improve existing algorithms for the enumeration of finite commutative semigroups. As an application 11,545,843 distinct commutative semigroups of order 9 were found.