伪补MS-代数的同余关系

本文研究了伪补MS-代数的同余关系.利用正则滤子和伪补代数的对偶窄间理论,得到了正则滤子所生成的同余关系的性质以及同余可换的伪补MS-代数类,从而推广了文献[9]的结果.     

MS代数的极大同态象

该文找到了MS代数的商代数分别为De Morgan代数、Boole代数及Stone代数的最小同余关系,并借助MS代数的对偶理论,得到了MS代数的极大同态象的对偶表示.     

KERNEL IDEALS AND CONGRUENCES ON MS-ALGEBRAS

In this article, the authors describe the largest congruence induced by a kernel ideal of an MS-algebra and characterize those MS-algebras on which all the congruences are in a one-to-one correspondence with the kernel ideals.     

Congruence permutable MS-algebras

We characterize the congruence permutable MS-algebras in a result analogous to that of Nachbin for distributive lattices. In our main result we prove, among other things, that the congruence permutability of an MS-algebra L is equivalent to the existence of two binary operations in L which satisfy certain equational properties. We show that the class of all congruence permutable MS-algebras with these additional operations forms an equational class. Finally we give a Mal’cev term for this new variety. Presented by J. Berman. Received May 12, 2005; accepted in final form November 5, 2005. Research supported by ANPCyT (Contrato Préstamo BID 1201/OC-AR) and SECyT (UNC)     

On symmetric extended MS-algebras whose congruences are permutable

Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized.     

具有逆断面的正则半群的同余的表示

具有道断面S°的正则半群可表示为有Saito's结构的半群W（I，S°，Λ，*，α，β）.我们利用由I，S°和Λ上的同余构成的所谓同余聚抽象地表示这类半群上的同余，进而给出了这类半群的同态象的构造法．     

Representation of congruences on regular semigroups with inverse transversals

For a regular semigroup with an inverse transversal, we have Saito’s structureW(I,S ^o, Λ, *, {α, β}). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of congruences on the structure component partsI,S ^o and Λ. The structure of images of this type of semigroups is also presented. This work is supported by Natural Science Foundation of Guangdong Province     

The overpartition function modulo small powers of 2

In a recent paper, Fortin et al. (Jagged Partitions, arXivmath. CO/0310079, 2003) found congruences modulo powers of 2 for the values of the overpartition function in arithmetic progressions. The moduli for these congruences ranged as high as 64. This note shows that for a set of integers of arithmetic density 1.     

幂格的同余关系

研究分配格的幂格的同余关系,给出幂格的同余关系格的一些重要性质,并得到幂格的一个同余类和同余关系格的两个交半格。     

K11-代数的主同余关系的可补性

研究K11-代数的主同余关系的可补性,给出K11-代数的主同余关系是可补的充要条件。     

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．     

Computing congruence lattices of finite lattices

An inequality between the number of coverings in the ordered set of join irreducible congruences on a lattice and the size of is given. Using this inequality it is shown that this ordered set can be computed in time , where .

     

集对代数软代数的集对表示

指出文[1]中的软代数表示定理（定理2．2）的错误,给出修改后的软代数表示定理。另外,讨论了集对代数的理想、同余关系和同余理想。     

Congruence lattices of algebras--- the signed labelling

For an arbitrary algebra a new labelling, called the signed labelling, of the Hasse diagram of is described. Under the signed labelling, each edge of the Hasse diagram of receives a label from the set . The signed labelling depends completely on a subset of the unary polynomials of and its inspiration comes from semigroup theory. For finite algebras, the signed labelling complements the labelled congruence lattices of tame congruence theory (TCT). It provides a different kind of information about those algebras than the TCT labelling particularly with regard to congruence semimodularity. The main result of this paper shows that the congruence lattice of any algebra admits a natural join congruence, denoted , such that satisfies the semimodular law. In an application of that result, it is shown that for a regular semigroup , for which in , is actually a lattice congruence, coincides with , and satisfies the semimodular law.

     

Quadratic forms and congruences for ℓ-regular partitions modulo 3, 5 and 7

Let $b_{\ell }(n)$ be the number of ℓ-regular partitions of n. We show that the generating functions of $b_{\ell }(n)$ with $\ell =3,5,6,7$ and 10 are congruent to the products of two items of Ramanujan's theta functions $\psi (q)$, $f(-q)$ and ${(q;q)}_{\infty }^3$ modulo 3, 5 and 7. So we can express these generating functions as double summations in q. Based on the properties of binary quadratic forms, we obtain vanishing properties of the coefficients of these series. This leads to several infinite families of congruences for $b_{\ell }(n)$ modulo 3, 5 and 7.     

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。     

W－理想与W－软代数

本文给出了Ｗ－理想与Ｗ－软代数的定义，主要结果有（Ⅰ）：（ｄ］，（ｄ＿１］分别是软代数Ｆ的同余理想，ｄ＿１≥ｄ，若（ｄ］是Ｗ－理想，则（ｄ＿１］是Ｗ－理想。（Ⅱ）：分别给出了软代数Ｆ，商软代数Ｆ／θ、软代数的直积Ｆ＝ПＦ＿ｉ是Ｗ－软代数的充分必要条件。     

The Strong Endomorphism Kernel Property in Ockham Algebras

An endomorphism on an algebra 𝒜 is said to be “strong” if it is compatible with every congruence on 𝒜; and 𝒜 is said to have the “strong endomorphism kernel property” if every congruence on 𝒜, different from the universal congruence, is the kernel of a strong endomorphism on 𝒜. Here we consider this property in the context of Ockham algebras. In particular, for those MS-algebras that have this property we describe the structure of their dual space in terms of 1-point compactifications of discrete spaces.     

A Characterization for Windowed Fourier Orthonormal Basis with Compact Support

Let g(x) ∈L ²(R) and ğ(ω) be the Fourier transform of g(x). Define g _mn (x) = e ^imx g(x−2πn). In this paper we shall give a sufficient and necessary condition under which {g _mn (x)} constitutes an orthonormal basis of L ²(R) for compactly supported g(ω) or ˘(ω). Received March 25, 1999, Revised November 5, 1999, Accepted September 6, 2000