关于G逆半群的同余格

本文讨论Ｇ逆半群上的同余,文中给出刻划ｐ＾ｋ,ｐｋ,ｐ＾Ｔ,ｐＴ的方法,并用来讨论半格同余,纯幂同余,群同余及幂等元分离同余。     

一类阿基米德半群的构造及其同余格

本文引入同底的π-左、右零半群的夹群积并用来刻划带本原幂等元的阿基米德半群的构造.文中讨论了有限阶阿基米德半群的同余格,并证明了当有限阶阿基米德半群的正则R,L类的个数不超过5时,它的同余格是半模格.     

π－纯整半群的局部化及应用

本文证明π－纯整半群在其幂等元带上的局部化存在且同构于其极大群同态象，由此，得出对应的最小群同余．     

亚纯正半群上的同余

本文讨论了亚纯正半群S上特殊同余间的关系.利用超迹和核给出了S上任一同余与特殊同余的关系及与群同余并的等式.用核正规系刻画了S上的极大幂等分离同余,得到了S/μ同构于E的几个等价条件.     

幂等元位于中心的半群的局部化和最小幂幺半群同余

局部化是交换代数的重要工具[1],证明幂等元位于中心的半群在其幂等元半格上的局部化存在且唯一,并给出此类半群的最小幂幺半群同余.另外,给出了若干半群的重要同余的刻划.     

π-纯正半群的r-半素矩形群同余

主要讨论π-纯正半群的r-半素矩形群同余和同余对之间的关系,并且找到了在r-半素矩形群同余的集合到r-半素矩形群同余对的集合之间的一一对应.     

-正则半群上的同余

刻划-正则半群上的如下同余:包括在中的最大同余、最大幂等元分离同余、(最小)基本强-同余和群同余。     

P-完全正则半群

求证具有强半格结构的完全正则半群成为P-完全正则半群的充分条件.利用半群的强半格结构以及同余的性质.完全单半群的强半格-正规群带是P-完全正则半群.矩形群的强半格正规纯正群类ONBG,左群的强半格左正规纯整群类LONBG,群的强半格Clifford半群类,矩形带的强半格正规带类NB,都具有性质P.     

幂交半格上的交同余及其性质

给出了幂交半格上几个具体的交同余,证明了任意多个交同余的并是交同余,并指出幂交半格的交同余类是子交半格,介绍了幂交半格上由θ诱导的交同余具有保并性和保序性。     

D—正则半群上的同余

刻划Ｄ－正则半群上的如下同余：包括在Ｄ［Ｒ］中的最大同余、最大幂等元分离同余、（最小）基本强Ｄ－同余和群同余。     

On the Structure of Cryptogroups

In this paper, we give a structure theorem for cryptogroups by means of bands and homomorphisms between completely simple semigroups.     

Characterizations of certain completely regular varieties

We characterize orthogroups, local orthogroups and (left,right) cryptogroups within completely regular semigroups by means of absence of certain kind of subsemigroups. For each of these varieties V, we determine the complete set of minimal non-V -varieties. For each of the latter varieties, we determine the lattice of its subvarieties. We then give a generating semigroup and a basis of its identities for every variety which occurs in this way. The subvariety lattices are illustrated by three diagrams.     

密码群的若干性质

In this paper, we give some characterizations of(regular, normal) cryptogroups with Green's relations, left(right) translations and homomorphisms.     

Characterizations of certain completely regular varieties

Abstract. We characterize orthogroups, local orthogroups and (left,right) cryptogroups within completely regular semigroups by means of absence of certain kind of subsemigroups. For each of these varieties V , we determine the complete set of minimal non-V -varieties. For each of the latter varieties, we determine the lattice of its subvarieties. We then give a generating semigroup and a basis of its identities for every variety which occurs in this way. The subvariety lattices are illustrated by three diagrams.     

S-Classification of Regular Semigroups

On any regular semigroup S, the greatest idempotent pure congruence τ the greatest idempotent separating congruence μ and the least band congruence β are used to give the S-classification of regular semigroups as follows. These congruences generate a sublattice Λ of the congruence lattice C(S) of S. We consider the triples (Λ,K,T), where K and T are the restrictions of the K- and T-relations on C(S) to Λ. Such triples are characterized abstractly and form the objects of a category S whose morphisms are surjective K- and T-preserving homomorphisms subject to a mild condition. The class of regular semigroups is made into a category S whose morphisms are fairly restricted homomorphisms. The main result of the paper is the existence of a representative functor from S to S. The effect of the S-classification on Reilly semigroups and cryptogroups is discussed briefly.     

Theorie des ecoulements dans les graphes orientes sans circuit

The paper deals with tournaments (i.e., with trichotomic relations) and their homomorphisms. The study of tournaments by means of their homomorphisms is natural as tournaments are algebras of a special kind. We prove (1) theorems which relate combinatorial and algebraic notions (e.g., the score of a tournament and the monoid of its endomorphisms); (2) theorems concerned with strictly algebraic aspects of tournaments (e.g., characterizing the lattice of congruences of a tournament). Our main result is that the group of automorphisms and the lattice of congruences of a tournament are in general independent. In the last part of the paper we give some examples and applications to other fields.     

纯正半群上的同余扩张(二)

刻画半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题（参见［1－5］）本文在[6]讨论了带上的同余的正规性和不变性以及在其Hall半群上的扩张的基础上,从同余扩张的角度刻划了完全正则的纯正半群的特征（定理26）,给出了一个纯正半群的带上的所有同余都可以扩张到这个纯正半群的充分必要条件．