L—逆左系对幺半群的刻画

正则左Ｓ－系是ｖｏｎ ｎｅｕｍａｎｎ正则半群的自然推广，逆左Ｓ－系是逆半群的自然扩广，作为左逆半群的自然推广，本文引入了Ｌ－逆左系的概念，并用来刻画了几类幺半群，如左逆幺半群，逆幺半群，ａｄｅｑｕａｔｅ幺半群等。     

强π-逆半直积

给出两个半群S和T的半直积是强π-逆半群，强π-E-酉逆半群和E-酉逆半群的充要条件，同时还讨论了E-酉逆半群的最小群同余与半直积的最小群同余之间的关系。     

关于G逆半群的构造

本文讨论一类重要的半群即Ｇ逆半群,文中给出Ｇ逆半群的主要的几例子,并详尽地讨论了Ｇ逆半群的构造。     

模右逆半群

半群的格方法－通过研究半群的子半群格来研究半群的特征和结构，与幂等元方法是研究半群的两种有效方法，本文利用这两种方法，完全确定了具有模的全右逆子半群的右逆半群的结构。     

Γ—正则半群上的若干同余

本文首先给出了Γ－正则半群上的群同余刻划。然后定义了Γ－逆半群的幂等分离核正规系，证明了Γ－逆半群上的幂等分离核正规系决定一个Γ－逆半群上的等分离同余，及Γ－逆半群上的幂等分离同余核是一个等分离核正规系。     

一类π正则半群的特征

引入了强右π逆半群的概念，讨论了它的特征，得到了这类半群的几个等价条件。     

Ⅱ正则半群的幂等元同余类

本文分别给出Ⅱ正则半群的幂等元同余类和Ⅱｏｒｔｈｏｄｏｘ半群的幂等元同余类的Ⅱ正则性刻画，其次，证明Ⅱ逆半群或完全Ⅱ逆半群或完全Ⅱ正则半群Ｓ的幂等元同余类是Ｓ的Ⅱ正则子半群。最后讨论ｏｒｈｔｏｄｏｘ半群的幂等元同余类的正则性。     

*-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.     

π-逆子半群格是模格的π-逆半群

π－逆半群是广义正则半群，研究它的π－逆子半群格是非常自然的．本文首先讨论了一个π－逆半群的π逆子半群格的直积分解;然后通过引进πU－链的概念刻划了π－逆子半群格是模格的π－逆半群的性质及特征．     

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.     

On Legal Semigroups

A new class of semigroups with a two variable regularity law is introduced. These semigroups are non-regular semigroups but they are closely related to regular semigroups. The local and global structures of this class of semigroups are investigated.AMS Subject Classification (2000): 20M10Partially supported by a Chinese University of Hong Kong Direct Research grant, Hong Kong (98/99) # 2060152.Partially supported by a grant of the National Science Foundation, China.     

Free orthodox semigroups and free bands with inverse transversals

It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST. In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST. Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.     

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。     

ON THE STRUCTURE OF REGULAR CRYPTO SEMIGROUPS

Superabundant semigroups are generalizations of completely regular semigroups written the class of abundant semigroups. It has been shown by Fountain that an abundant semigroup is superabundant if and only if it is a semilattice of completely J ^*-simple semigroups. Reilly and Petrich called a semigroup S cryptic if the Green's relation H is a congruence on S. In this paper, we call a superabundant semigroup S a regular crypto semigroup if H ^* is a congruence on S such that S/H ^* is a regular band. It will be proved that a superabundant semigroup S is a regular crypto semigroup if and only if S is a refined semilattice of completely J ^*-simple semigroups. Thus, regular crypto semigroups are generalization of the cryptic semigroups as well as abundant semigroups.     

带逆断面的正则半群上的强模糊同余

带逆断面的正则半群是一类重要的正则半群.就带逆断面的正则半群类引入强模糊同余的概念,进而用所谓的强模糊同余三元组抽象地刻画带逆断面的正则半群上的强模糊同余.     

Inverse semigroups determined by their lattices of convex inverse subsemigroups I

Every inverse semigroup possesses a natural partial order and therefore convexity with respect to this order is of interest. We study the extent to which an inverse semigroup is determined by its lattice of convex inverse subsemigroups; that is, if the lattices of two inverse semigroups are isomorphic, how are the semigroups related? We solve this problem completely for semilattices and for inverse semigroups in general reduce it to the case where the lattice isomorphism induces an isomorphism between the semilattices of idempotents of the semigroups. For many inverse semigroups, such as the monogenic ones, this case is the only one that can occur. In Part II, a study of the reduced case enables us to prove that many inverse semigroups, such as the free ones, are strictly determined by their lattices of convex inverse subsemigroups, and to show that the answer obtained here for semilattices can be extended to a broad class of inverse semigroups, including all finite, aperiodic ones. Received September 24, 2002; accepted in final form December 15, 2002.     

Algebras of Ehresmann semigroups and categories

E-Ehresmann semigroups are a commonly studied generalization of inverse semigroups. They are closely related to Ehresmann categories in the same way that inverse semigroups are related to inductive groupoids. We prove that under some finiteness condition, the semigroup algebra of an E-Ehresmann semigroup is isomorphic to the category algebra of the corresponding Ehresmann category. This generalizes a result of Steinberg who proved this isomorphism for inverse semigroups and inductive groupoids and a result of Guo and Chen who proved it for ample semigroups. We also characterize E-Ehresmann semigroups whose corresponding Ehresmann category is an EI-category and give some natural examples.     

关于两类特殊的代数

本文对泛代数中两类代作了一些研究，得到一些结果，并且讨论了这两类代数在半群中的应用。