真理想为Archimedean子半群的偏序半群

根据真理想情况给出了偏序半群的一种分类，研究了真理想为Archimedean子半群的偏序半群的特征．     

富足半群上的自然偏序

本文研究富足半群上的自然偏序，得到Green关系和自然偏序之间的联系，确定了富足半群何时关于自然偏序具有单边(双边)相容，另外，也研究了富足半群的本原元。     

偏序半群的最大自然序半格同态象

引进了自然序半格，偏序半群的自然序半格同态象和二次主根基等概念，利用二次主根基构造出了任意偏序半群的最大自然序半格同态象。     

抽象半线性泛函微分方程正胡的存在性

本利用算子半群理论和锥压缩不动点定理,在合适的条件下建立了偏序Banach空间中半线性泛函数微分方程全局正解的存在性。     

半群上的拓扑、偏序和相关Domain

在半群G上引入了半群拓扑O[G]和半群偏序≤G,研究了它们的性质和相互联系,得到如下主要结论:(1)拓扑空间(G,O[G])中开集均为偏序集(G,≤G)的下集;(2)拓扑空间(G,O[G])为T,的当且仅当O[G]是离散的,当且仅当G中任意元是幂等元;(3)在集合包含序下O[G]为代数的完全分配格;(4)若(G,O[G])是T0空间,则O[G]是偏序集(G,≤G)上的对偶Alexandrov拓扑;(5)半群G是伪有限的当且仅当偏序集(G,≤Gop)是代数Domain.     

乘法半群为左正规纯正群的半环

研究了加法半群为半格,乘法半群为左正规纯正群的半环．证明了此类半环（S,＋,．）可以嵌入到半格（S,＋）的自同态半环中．构造S的一个特定的偏序关系,得到了（S,·）上的自然偏序与所构造偏序相等的等价条件．     

自然序Dubreil-Jacotin富足半群

本文考虑Ｄｕｂｒｅｉｌ－Ｊａｃｏｔｉｎ富足半群,给出若干特征后,建立了自然序Ｄｕｂｒｅｉｌ－Ｊａｃｏｔｉｎ富足半群的结构,作为应用,给出了具有正则性条件的自然序Ｄｕｂｒｅｉｋｌ－Ｊａｃｏｔｉｎ富足半群的结构,并将结果推广到具有最大幂等元的自然序的偏序富足半群上。     

Hamilton半群的结构

每个子半群是左理想的半群，称为左Ｈａｍｉｌｔｏｎ半群，本文给出左Ｈａｍｉｌｔｏｎ半群的刻划，并将左Ｈａｍｉｌｔｏｎ半群表示为有向森林，最后给出左Ｈａｍｉｌｔｏｎ半群同构的充要条件。     

抽象半线性泛函微分方程正解的存在性

本文利用算子半群理论和锥压缩不动点定理 ,在合适的条件下建立了偏序 Banach空间中半线性泛函数微分方程全局正解的存在性     

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。     

On C-left Hyp erideals of Ordered Semihyp ergroups

In this paper, the concept of C-left hyperideals is introduced in ordered semihypergroups, and several related properties are investigated. In particular, we discuss the relationships between the greatest left hyperideals and C-left hyperideals of ordered semihypergroups. Furthermore, we introduce the concept of left bases of an ordered semihypergroup, and give out the sufficient and necessary conditions of the existence of the greatest C-left hyperideal of an ordered semihypergroup by the properties of left bases. The result about C-left ideals in ordered semigroups is generalized to the ordered semihypergroups.     

偏序半群的C-左理想

本文引入了偏序半群中Ｃ 左理想的概念，讨论了Ｃ 左理想的一些基本性质，定义了左基的概念并利用它给出了最大Ｃ 左理想存在的必要和充分条件．作为应用，本文还讨论了每个真左理想均为Ｃ 左理想和无Ｃ 左理想这两类半群的结构特征．本文的结果在一般半群中也成立     

On Ordered Semigroups Which are Semilattices of Simple and Regular Semigroups

We characterize the ordered semigroups which are decomposable into simple and regular components. We prove that each ordered semigroup which is both regular and intra-regular is decomposable into simple and regular semigroups, and the converse statement also holds. We also prove that an ordered semigroup S is both regular and intra-regular if and only if every bi-ideal of S is an intra-regular (resp. semisimple) subsemigroup of S. An ordered semigroup S is both regular and intra-regular if and only if the left (resp. right) ideals of S are right (resp. left) quasi-regular subsemigroups of S. We characterize the chains of simple and regular semigroups, and we prove that S is a complete semilattice of simple and regular semigroups if and only if S is a semilattice of simple and regular semigroups. While a semigroup which is both π-regular and intra-regular is a semilattice of simple and regular semigroups, this does not hold in ordered semigroups, in general.     

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.     

关于序半群的模糊拟理想

In this paper,fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets.Furthermore,we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals.Finally,we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-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.     

Split Left GC-Lpp Semigroups

A left GC-lpp semigroup S is called split if the natural homomorphism γb of S onto S/γ induced by γ is split.It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal.In particular,a construction theorem for split left GC-lpp semigroups is established.     

Some Characterizations of Strongly Semisimple Ordered Semigroups

In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup $S$ is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of $S$. In particular, we prove that $S$ is strongly semisimple if and only if each fuzzy left ideal of $S$ is the intersection of all quasi-prime fuzzy left ideals of $S$ containing it.     

关于强可逆半准素序半群

把由G．Thierrin和A．Spoletini-Cherubini等人定义并研究的强可逆半群以及由S．Bogdanovic研究的半准素半群分别推广为强可逆序半群和半准素序半群．分别给出了半准素序半群和强可逆序半群类中的半准素序半群的刻划，还给出了其所有理想是素理想的强可逆序半群的刻划．