纯正半群上的同余扩张(一)

刻划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．本文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，从同余扩张的角度刻划了带上的同余的性质，给出了扩张的极大、极小同余的描述．     

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 .     

双重Stone代数的主同余关系

给出了双重Stone代数的主同余关系θ(a,b)(a≤b)的等式刻划以及其它的一些性质,由此得到了主同余关系θ(a,b)(a≤b)存在Boo le-补的若干充分条件.     

Principal Congruence Subgroups of Hecke Groups H（√q）

Using the notion of quadratic reciprocity, we discuss the principal congruence subgroups of the Hecke groups H（√q）,q 〉 5 prime number.     

一些同余问题的例外集合

利用特征和与指数和的估计,研究了一些同余问题的例外集合.具体来说,设p为充分大的素数,集合Y■Zp,正整数N相似文献