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.     

Fuzzy同余和正规Fuzzy子群(英文)

自从A. Rosenfeld在1971年提出Fuzzy子群的概念以来,在Fuzzy群的研究方面已有不少进展,例如见[1,2,5,6,10,11,14]。另一方面,L.A.Zadeh首创的Fuzzy关系理论的研究也是硕果累累,例如见[3,4,8,12,13,15]。本文通过Fuzzy同余关系和正规Fuzzy子群的相互联系,将这两个方向的研究成果进行“嫁接”和“杂交”,得到许多有趣的结果。主要结果是定理2.7,定理3.1和3.6。本文另一主题是引入T-Fuzzy群的正规T-Fuzzy子群的新概念,当T是正则t-范算子时,得到了T-Fuzzy群的三个同构定理,作者认为它比现有的相应同构定理更为简洁、广泛和自然。     

软代数的素M－理想与同余关系

在文［１］中，裴礼文教授引入了软代数的Ｍ－理想的概念。本文在此基础上，定义了对偶Ｍ－理想、素Ｍ－理想、素对偶Ｍ－理想等概念。并讨论了它们的若干性质及相互关系。证明了由一素Ｍ－理想，可确定软代数Ｌ的一个同余关系，这时Ｌ可同态于一个四元软代数或一三元软代数。     

|C(S)/L|≤2的完全正则半群

刻画了|C(S)/L|≤2的完全正则半群S的同余格的具体特征,给出了具有上述性质的所有完全正则半群的分类.     

A simple proof of a curious congruence by Zhao

The author gives a simple proof of the following curious congruence for odd prime 3$"> which was established by Jianqiang Zhao:

0}}}\frac{1}{ijk}\equiv -2B_{p-3}(\text{mod} p).\end{displaymath}">

     

Some Categorical Algebraic Properties: Counter-Examples for Functor Categories

This work is a complement to the authors earlier papers, where it is shown that a functor category inherits from such properties as amalgamation, transferability and congruence extension if has either products or certain pushouts. A general scheme is given for constructing counter-examples which show that the latter condition on is essential. In particular, it is shown that the functor categories , , ( resp.) do not satisfy the amalgamation (congruence extension resp.) property in general. Moreover, one class of categories is described, where the condition of the existence of certain pushouts is not only sufficient, but also necessary for to preserve the considered properties of .Mathematics Subject Classifications (2000) 18A25, 18A32, 18B99, 08B26.Dali Zangurashvili: The support rendered by INTAS Grant 97 31961 is gratefully acknowledged.     

Jagged Partitions

By jagged partitions we refer to an ordered collection of non-negative integers (n₁, n₂,..., n_m) with n_m≥ p for some positive integer p, further subject to some weakly decreasing conditions that prevent them for being genuine partitions. The case analyzed in greater detail here corresponds to p = 1 and the following conditions n_i≥ n_i+1−1 and n_i≥ n_i+2. A number of properties for the corresponding partition function are derived, including rather remarkable congruence relations. An interesting application of jagged partitions concerns the derivation of generating functions for enumerating partitions with special restrictions, a point that is illustrated with various examples. 2000 Mathematics Subject Classification: Primary—05A15, 05A17, 05A19     

On Uniquely Complemented Posets

In this paper, some classical results of uniquely complemented lattices are extended to uniquely complemented posets (with 0 and 1) like Peirce's Theorem, the Birkhoff–von Neumann Theorem, the Birkhoff–Ward Theorem. Further, it is shown that a section semi-complemented pseudocomplemented poset is a Boolean poset. Mathematics Subject Classification (2001) 06A06, 06A11, 06C15, 06C20, 06D15     

Groups associated with minimal flows

Let S be topological semigroup, we consider an appropriate semigroup compactification of S. In this paper we study the connection between subgroups of a maximal group in a minimal left ideal of , which arise as equivalence classes of some closed left congruence, and the minimal ow characterized by the left congruence. A particular topology is defined on a maximal group and it is shown that a closed subgroup under this topology is precisely the intersection of an equivalence class with the maximal group for some left congruence on .