关于模格、分配格充要条件的严格推证

The Proof on Necessary and Sufficient Condition of a Lattice being Modular Lattice and Distributive Lattice

本文在离散数学的范围内,从格、子格、模格、分配格的定义,格的运算性质出发,充分利用两个特殊的五元格,对有关格是模格、格是分配格的充分与必要条件的五个定理作出严格的推证。

Five theorems on the necessary and sufficient conditions are proved strictly,which are about a lattice being modular lattice,a lattice being distributivelattice and a modular lattice being distributive lattice.This work is based on the definitions of lattice,sublattice,modular lattice and distributive lattice and on the operating character of lattice within the extent of discrete matbematies.