关于一致半格的注记

A note on uniform semilattices

首先证明了满足极大条件的无限链一定是一致半格.其次,通过探究一致半格与极大条件之间的关系,给出了一致半格为满足极大条件的无限链的充分必要条件.最后,讨论了一致半格与极小条件以及反一致半格与极大条件之间的内在关系,并且给出了相应的例子.

In this paper,the infinite chain which satisfies the maximal condition must be a uniform semilattice is proved.By exploring the relationship between the uniform semilattice and the maximal condition,the necessary and sufficient conditions of the uniform semilattice is the infinite chain satisfying the maximal condition are given.Finally,the relation between the uniform semilattice and the minimal condition and the relation between the antiuniform semilattice and the maximal condition are discussed,and the corresponding examples are given.