摘要
众所周知,格L的任意一个素理想集都确定L的一个同余关系。本文讨论了相反的问题,指出仅当L是分配格时才能用素理想集确定其每个同余关系。进一步又证明了分配格的同余关系格可嵌入于它的素理想集的对偶幂集格。本文最后还给出了上述嵌入是同构的充分必要条件为L是局部有限的。
For a latlice L,let (L) denote the set of all prime ideals of L, and C(L)be the congruence latlice of L. It is well known that given a subset A of (L),we can construct a congrvence relation θ_A of L:x≡y (θ_A) iff for every P∈A, either x,y∈or x,y∈L—P(See [1]P_(76)). In this paper,we consider the congruence relations determined by the sets of prime ideals. First,we show that L is a distributive latlice if and only if for any congruence relation θ of L, there is at least one subset A(L) ,such that θ=θ_A. Furthermore we embed C(L) into the latlice P((L)),the dual of the power set of (L). In the last section of this paper, we also show that for a distributive latlice L,C(L)≌P((L)) if and only if L is locally finite. This result is seen to be a generalization of a result of [3].
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
1989年第1期26-29,共4页
Journal of Inner Mongolia University：Natural Science Edition
关键词
分配格
同余关系
素理想
Distributive lattices
Congruence relations
Prime ideals
