格中两类分配等式的关系研究  

On the Relation of Two Types of Distributive Equality in Lattice

作　　者：郭芸[1] 王朝晖[1] 

机构地区：[1]苏州大学计算机科学与技术学院,江苏苏州215006

出　　处：《数学的实践与认识》2013年第6期262-266,共5页Mathematics in Practice and Theory

基　　金：苏州市应用基础研究计划(SYG201116);苏州大学教改项目

摘　　要：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.With the conclusion presented in the classic discrete mathematics textbook that the distributive equality of intersection with union is equivalent to the equality of union with intersection, a common wrong proof is analyzed and a counter example is given to show the conclusion is not necessarily true in general lattice. Furthermore, the two types of distributive equality are proved to be equivalent in and only in modular lattice and an easier algorithm in judging whether a modular lattice is a distributive one by definition is put forward. As an application of all the results above, a new proof of one theorem in the textbook is given.

关 键 词：格 模格 分配格 分配等式 等价 

分 类 号：O153.1[理学—数学]