格中一些等价性问题及其证明

Proof of some Equivalence Problems in the Lattice

证明了格的偏序定义与代数定义的等价性;证明了格中幂等律与吸收律的等价性;证明了分配格中分配律与消去律的等价性,这表明满足消去律是分配格的基本属性.

This paper proves lattice of partial order definition and equivalence of algebraic definition. Al- so, it proves lattice in the equivalence of idempotent law and absorption law. It proves a distributive lattice in the equivalence of distributive law and the cancellation law, too. This suggests that satisfying the cancellation law is the basic attributes of distributive lattice.