交换分配半环上的最小分配格同余

§ 1 .　Introduction　　AsemiringSisanalgebraicstructure(S ,+,·)consistingofanon emptysetStogetherwithtwobinaryoperations +and·onSsuchthat(S ,+)and(S ,·)aresemigroupsconnectedbyring likedistributivity[1 ] .AsemiringSiscalledacommutativesemiringif (S ,+)and(S ,·)arebothcommutative.AcommutativesemiringiscalledacommutativedistributivityifinStheadditionisdistributiveaboutmultiplication ,i.e.,ab +c =(a+c) (b+c) ,a +bc=(a +b) (a+c) holdsforalla ,b,c∈S[2 ] .Anequivalentrelationρonasemiring…     

分配伪补格的主理想

本文给出了分配伪补格 ( L;∧ ,∨ ,* ,0 ,1 )中的主理想 I=( d]成为同余理想的充分必要条件 .当 L是局部有限时 (即 d∈ S( L) ,Fd={x|x* * =d}有限 ) ,对骨架 S( L)中的每个元素 d,我们找到了以 I=( d]为核心的最小同余关系 ,利用以上结果我们得到一个 Stone代数是布尔代数的一些等价条件 .     

分配半环上的可除半环同余

§ 1.　Introduction　　AsemiringSisanalgebraicsystem (S ,+ ,·)consistingofanon_emptysetStogetherwithtwobinaryoperations +and·onSsuchthat (S ,+ )and (S ,·)aresemigrolupscon nectedbyring_likedistributivity .AsemiringSiscalleddistributiveifinStheadditionisdis tributiveaboutmultiplication ,i.e .ab+c=(a+c) (b +c)anda+bc=(a +b) (a+c)holdforalla ,b ,c∈S .AsemiringSiscalleddivisibleif(S ,·)isagroup .AnequivalencerelationρonasemiringSiscalledacongruenceonS ,iffρisacongruenceon (S ,+ )and (…     

半环的强分配格上的环同余

主要讨论了在一定条件下半环的强分配格S上的环同余ρ与半环族{Sα}α∈D上的环同余族{ρα}α∈D之间的关系.     

Distributive implication groupoids

We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.      

一类广义正则半环上可除半环同余的等价刻画

研究了一类广义正则半环的理想,利用这类理想,得到了这类半环上同余的几种刻画.     

Distributive Quantales

A concept of distributive quantale is introduced. It provides to extend some basic results of locale theory for quantales.     

关于分配格的判定问题

针对分配格判定时容易出错这一教学难题,提出可以利用学生专业特点从而结合计算机这一工具来帮助解决,并通过一个典型例子来具体说明,该例子同时也指出了教材习题解答书中的一处错误.认为本文提出的这一教学思想对于离散数学的教学有一定的启示.     

分配格上矩阵的特征向量

主要讨论分配格上的矩阵A的标准特征向量问题.从基本概念出发,给出了全部标准特征向量的计算方法。     

格中两类分配等式的关系研究

针对离散数学经典教材中提出的"交运算对并运算的分配等式和并运算对交运算的分配等式是等价的"这一结论,分析了一种常见的错误证明,通过一个反例说明该结论在一般的格中不一定成立,进一步证明这两个分配等式在且仅在模格中是等价的,并提出利用定义判断一个模格是否是分配格的简便算法.作为一个应用,重新证明了该教材中的一条定理.     

分配P-代数中的0-理想

本文对分配Ｐ－代数中的０－理想进行了初步探讨．给出了０－理想的刻画并利用它得到了一些结果     

Quasiorders and Sublattices of Distributive Lattices

We study the lattice of all (0,1)-sublattices of a distributive lattice L, using certain compatible quasiorders on the Priestley space of L as our principal tool. Special emphasis is put on the case of finite L, where epic sublattices, Frattini sublattices and covers are considered in some detail. We hope to demonstrate that quasiorders may serve as a concept suitable to unify the many different representations of sublattices of L which are found in the literature.     

Usort: An efficient hybrid of Distributive Partitioning Sorting

A new hybrid of Distributive Partitioning Sorting is described and tested against Quicksort on uniformly distributed items. Pointer sort versions of both algorithms are also tested.     

双单子分配律的R-矩阵

本文讨论了双单子分配律的表示及其R-矩阵结构.设F和G是给定的双单子,刻画了单子双模范畴,并给出了其为辫子范畴的充要条件,由此构造了量子YangBaxter方程的一组新解系.     

分配伪格上矩阵积和式的不等式

在分配伪格上研究矩阵的积和式问题,得到关于矩阵积和式的若干不等式.其结果推广了已有文献上的结论.     

Truncated Distributive Lattices: Conceptual Structures of Simple-Implicational Theories

Logical relationships in everyday human thought are predominantly inferences with one-element premises. This becomes apparent in the practice of Formal Concept Analysis by the frequent occurrence of truncated distributive lattices as concept lattices. This paper gives a mathematization of the underlying everyday theories of logical relationships and elaborates useful mathematical results, in particular about algorithmically drawing concept lattices which correspond to the everyday logical theories. This revised version was published online in June 2006 with corrections to the Cover Date.     

分配P-代数的核理想与余核滤子

本文的主要结果是给出了分配P-代数中一个理想成为核理想的充要条件,同时提出了余核滤子的概念,研究了核理想与余核滤子之间的某些内在联系.     

Definable principal subcongruences

For varieties of algebras, we present the property of having "definable principal subcongruences" (DPSC), generalizing the concept of having definable principal congruences. It is shown that if a locally finite variety V of finite type has DPSC, then V has a finite equational basis if and only if its class of subdirectly irreducible members is finitely axiomatizable. As an application, we prove that if A is a finite algebra of finite type whose variety V(A) is congruence distributive, then V(A) has DPSC. Thus we obtain a new proof of the finite basis theorem for such varieties. In contrast, it is shown that the group variety V(S ₃ ) does not have DPSC. Received May 9 2000; accepted in final form April 26, 2001.     

分配格中理想诱导的幂格

本文在文 [1 ]的基础上 ,给出由分配格中理想诱导的两种幂格 .     

完全分配CSL代数上的中心化子

设L是可分Hilbert空间上的完全分配交换子空间格,A是Alg L的子代数并且包含Alg L的全体有限秩算子.主要结果是:(1)A上的中心化子是拟空间的;(2)Alg L上的Jordan中心化子是中心化子;(3)当L是套时,Alg L上的Lie中心化子可表示成一个中心化子与一个可加泛函之和的形式,该泛函作用在形如AB-BA的算子上为零.