正则半群上的广义逆半群同余

利用同余的核与超迹描述正则半群上的广义逆半群同余。     

正则半群的左Clifford同余

本文给出了左 Clifford 半群的一个等价条件,研究了正则半群上的左 Clifford同余,用同余的核和同余的超迹描述了左 Clifford 同余,右 Clifford 同余和 Clifford 同余。     

序半群中的最小完全半素序理想

在序半群上定义了几种新的关系,利用它们得到了序半群上最小完全半素理想的结构,并以此给出了序半群的最小正则半格同余的另一种描述,所得结果是Miroslav Ciric在文[1]中的部分结果向序半群上的推广。     

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。     

φ-正则半群上的φ-同余(英文)

给出了-正则半群内的-核正规系统的一个等价刻划并用-核正规系统描述了-正则半群上的强-同余．     

正则纯整群带的算子半群和同余网

正则半群Ｓ的同余格（Ｓ）上的算子Ｋ，ｋ，Ｔ和ｔ定义如下：对于ρ∈Ｓ，ρＫ和ρｋ（ρＴ和ρｔ）分别是与ρ有相同核（迹）的最大和最小同余．我们确定了所有正则纯整群带的同余格上由Ｋ，ｋ，Ｔ和ｔ生成的算子半群．并确定了正则纯整群带上任意同余的同余网．     

弱Clifford形正则半群的半直积和圈积

本文给出两个么半群Ｓ和Ｔ的半直积和圈积为弱Ｃｌｉｆｆｏｒｄ拟正则么半群的充要条件和半直积的结构，同时还讨论了弱Ｃｌｉｆｆｏｒｄ拟正则么半群的最小群同余与半直积的最小群同余之间的关系。     

正则Г—半群上的纯正同余

定义了正Г－半群上的Ｓａｎｄｗｉｃｈ集合及纯正同余对，然后刻划了正则Г－半群上纯正同余。     

正则Γ-半群上的纯正同余

定义了正则Γ－半群上的Ｓａｎｄｗｉｃｈ集合及纯正同余对，然后刻划了正则Γ－半群上的纯正同余．     

拟正则半群上的完全正则同余

拟正则半群上的两个完全正则同余相等当且仅当它们的核正规系相同。更进一步地,我们还可建立一个从一个拟正半群上的全体完全正则同余的集合到这个半群的所有完全正则核正规系的集合上的双射。     

Congruences on *-Regular Semigroups

In this paper we study the congruences of *-regular semigroups, involution semigroups in which every element is p-related to a projection (an idempotent fixed by the involution). The class of *-regular semigroups was introduced by Drazin in 1979, as the involutorial counterpart of regular semigroups. In the standard approach to *-regular semigroup congruences, one ,starts with idempotents, i.e. with traces and kernels in the underlying regular semigroup, builds congruences of that semigroup, and filters those congruences which preserve the involution. Our approach, however, is more evenhanded with respect to the fundamental operations of *-regular semigroups. We show that idempotents can be replaced by projections when one passes from regular to *-regular semigroup congruences. Following the trace-kernel balanced view of Pastijn and Petrich, we prove that an appropriate equivalence on the set of projections (the *-trace) and the set of all elements equivalent to projections (the *-kernel) fully suffice to reconstruct an (involution-preserving) congruence of a *-regular semigroup. Also, we obtain some conclusions about the lattice of congruences of a *-regular semigroup. This revised version was published online in June 2006 with corrections to the Cover Date.     

Orthodox Congruences on An Eventually Regular Semigroup

It is shown that each regular congruence on an eventually regular semigroup is uniquely determined by its kernel and hyper-trace. Furthermore, the orthodox congruences (resp., the regular congruences ) on an eventually regular (resp., orthodox) semigroup S are described by means of certain congruence pair (ξ, K), where ξ is a certain normal congruence on the subsemigroup 〈E(S)〉 generated by E(S) and K is a certain normal subsemigroup of S.     

On Hopf Algebras with Nonzero Integral

Let S be the model of a semigroup with an associate subgroup whose identity is a medial idempotent constructed by Blyth and Martins considered as a unary semigroup. For another such semigroup T, we construct all unary homomorphisms of S into T in terms of their parameters. On S we construct all unary congruences again directly from its parameters. This construction leads to a characterization of congruences in terms of kernels and traces. We describe the K, T, L, U and V relations on the lattice of all unary congruences on S, again in terms of parameters of S.     

序半群的一类正则同余

设S是有向序半群,本文给出了S上的一类正则同余,称为强序同余的定义及性质.证明了S的强序同余是强正则同余,但反之不成立.同时证明了强序同余格SOC(S)是S的同余格C(S)关于通常集合的交和传递积的V-完备的分配子格.     

纯正半群上若干同余的刻划(英文)

本文在纯正半群上首先引入了关系ρｍｉｎ,ρｍａｘ,ρｍｉｎ和ρｍａｘ,刻划了纯正半群上一般同余的迹类。然后利用核－迹方法给出了纯正半群上几类特殊同余的等价刻划。在此基础上,进一步研究了各类同余间的相互联系,把逆半群上有关同余的若干结果推广到纯正半群上。     

On ℘-regular semigroups having regular *-transversals

Our aim is to investigate the properties and structure of the ℘-regular semigroups having regular *-transversals. We first give two kinds of definitions for regular *-transversals and prove that they are equivalent. A condition for two regular *-transversals of a ℘-regular semigroup to be isomorphic is given. The *-congruences on the ℘-regular semigroups having regular *-transversals are characterized by using the *-congruence triples. In particular, we describe the idempotent separating congruences and the group congruences on such ℘-regular semigroups.     

两类完全正则半群的同态和同余

本文研究了密群的同态和纯正群的幂等元分离同余.定义了密群的半格类之间的一种映射,利用该映射,半格的同态及完全单半群上的同态刻画了密群间的同态.利用群核正规系讨论了纯正群的幂等元分离同余.并给出其一种简单的表示形式.     

含幺Clifford半群上的Rees矩阵半群的同余和正规加密群结构

给出了含幺Clifford半群上的Rees矩阵半群S的正规加密群结构,证明了在含幺Clifford半群上的Rees矩阵半群S上以下两个条件是等价的:(1)S上的同余ρ是完全单半群同余;(2)S上的同余ρ和S上的相容组之间存在保序双射.最后还证明了S上的完全单半群同余所构成的同余格是半模的.