关于分配格的充要条件

On Necessary and Sufficient Conditions of Distributive Lattice

为了对分配格的本质属性作进一步地认识,依据格所具有的偏序结枸特征,运用了抽象代数的思维方法,以及严格的逻辑推理程序,得到了在一般格中的分配律和消去律是等价的这一结果,从而说明了消去律是分配格的本质属性.并且如果代数系统(A,+,*)的两个二元运算满足交换律,结合律和吸收律,则消去律和分配律等价.

On the basis of the fact that lattice is characterized by partial order structure,the paper draws a conclusion through the thinking mode of abstract algebra and a strict logical inference that the distributive law is equal in value to the cancellation law in general lattice. This indicates that the cancellation law is the elementary property of the distributire lattice,and that if the binary operation of the algebric system（A,＋,＊） satisfies the commutative law, the integral law and the absorption law, then the cancetation law is equal in value to the distributive law.