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。     

关于同余交换纯正群并的构造与分类

本文讨论同余交换纯正群并的构造与分类。文中将该类半群给出分解方法，指出该类半群是它的左，右分量的织积。接着给出该类半群的完整分类，指出共有２０类并给出各类的构造，上述结论还用来讨论同余交换带，文中给出所有２９个同余交换带的构造并证明同余交换带都是有限的且元素个数不超过１３．     

有限R—平凡p—半群的分类

半群的代数理论的一个重要课题是研究半群S的同余的特性对于S的结构的影响。作为这个课题的一个方面是研究同余可交换半群的性质。本文借助有限R-平凡半群构造定理[5]来研究有限R-平凡的同余可交换半群的分类。设S是半群。S的同余格记为C(S)。设x∈S,ρ∈C(s),x所在的ρ-类记为xρ。S称为同余可交换半群(简称为P-半群),如果ρ°σ=σ°ρ     

超凸度量空间中非扩张可交换映象族的几乎不动点

获得了关于超凸度量空间中非扩张可交换映象族不动点存在性的更一般结果.证明了可数个非扩张可交换映象的公共ε-几乎不动点集的超凸性,并在一定条件下证明了任意个非扩张可交换映象的公共ε-几乎不动点集的超凸性.还讨论了Baillon的两个重要结果间的等价关系.     

关于矩阵秩的几点注记

研究了任意数域上两个相乘可交换方阵的幂的乘积的秩,推广了一个熟知的关于方阵幂的秩的结果.     

三个Hankel算子的交换性

本文研究并给出了 Hardy空间上三个Hankel算子可交换的一个充分必要条件,设f,g,u∈∩q＞1 Hq均为非常值函数,则Hf,Hg和Hu可交换当且仅当f,g,u中任意两个函数的非平凡的线性组合是常数.     

Hamilton群的主同余

研究了有限交换群和Hamilton群的主同余,利用同余的定义并构造它们的主同余公式,给出了它们的主同余刻画.     

图上Z~2可扩作用的非存在性

文[9]中作者考虑连续统上可扩群作用的存在性问题,证明了单位闭区间上不存在自由交换群Z×Z的可扩作用,并且给出一个例子表明闭区间上存在自由积Z*Z的可扩作用.换句话说,由两个交换同胚生成的群是不能可扩作用在闭区间上的,但还是存在由两个非交换同胚生成的群能够可扩作用在闭区间上.本文证明了图上不存在Z×Z的可扩作用,解决了文[9]所提的一个问题.     

软代数的理想和同余关系

本文刻划了使软代数Ｆ的任意二元ａ，ｂ在一个同余类的最小同余关系（定理１），Ｆ的理想可以成为某个同余关系的核的充分必要条件（定理２），以Ｆ的同余理想Ｉ为核的最小和最大的同余关系（定理３）．     

算术级数中的奇数Goldbach问题(Ⅱ)

本文考察了几乎所有模的算术级数中的奇数Goldbach问题．证明了对几乎所有的模r≤N1/6-ε,充分大的正奇数N可表为三个素数之和,其中每个素数取在模r 的满足必要同余条件的任意剩余系中．     

A construction of commutative nilsemigroups

All commutative nilsemigroups are constructed from congruences on free commutative semigroups.     

FINITE RINGS WITH COMMUTING NILPOTENT ELEMENTS

As a generalization of Wedderburn's theorem, Herstein [5] proved that a finite ring R is commutative, if all nilpotent elements are contained in the center of R. However a finite ring with commuting nilpotent elements is not necessarily commutative. Recently, in [9] and [10], Simons described the structure of finite rings R with J(R)² = 0 in a variety with definable principal congruences. In this paper, we will consider the difference between the finite commutative rings and the finite rings in which any two nilpotent elements commute with each other. As a consequence, we describe the structure of finite rings R with [J(R), J(R)] = 0 in a variety with definable principal congruences.     

Commutative Noetherian semigroups are finitely generated

We provide a short proof that a commutative semigroup is finitely generated if its lattice of congruences is Noetherian.     

Certain congruences on free trioids

Loday and Ronco introduced the notion of a trioid and constructed the free trioid of rank 1. This paper is devoted to the study of congruences on trioids. We characterize the least dimonoid congruences and the least semigroup congruence on the free (commutative, rectangular) trioid.     

Commutative Noetherian Semigroups are Finitely Generated

Abstract. We provide a short proof that a commutative semigroup is finitely generated if its lattice of congruences is Noetherian.     

Finiteness of lattice of congruences on commutative semigroups

It is well known that if an abelian group has a finite number of distinct congruences, then it is finite. This can be extended to commutative semigroups. Furthermore we see that the theorem is still true under weaker conditions.     

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.     

The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion

In this paper we study, the Reidemeister zeta function. We prove rationality and functional equations of the Reidemeister zeta function of an endomorphism of finite group. We also obtain these results for eventually commutative endomorphisms. These results are applied to the theory of Reidemeister and Nielsen numbers of self-maps of topological spaces. Our method is to identify the Reidemeister number of a group endomorphism with the number of fixed points in the unitary dual. As a consequence, we show that the Reidemeister torsion of the mapping torus of the unitary dual is a special value of the Reidemeister zeta function. We also prove certain congruences for Reidemeister numbers which are equivalent to a Euler product formula for the Reidemeister zeta function. The congruences are the same as those found by Dold for Lefschetz numbers.