同余关系格是完全Stone格的格

On Lattices whose Congruences Form Completely Stonean Lattices

本文主要研究具有完全Stone同余关系格的格,为此我们给出一个条件(S):称格L的真商u/v满足条件(S),如果对L的任意满足的真商a/b,c/d,存在真商x/y,满足通过条件(S),我们给出了格L的同余关系格C(L)的骨架S(C(L))中原子(如果存在)的形式及S(C(L))为原子格时格L的特征,最后我们得出本文的主要结果:格L的简余关系格C(L)是完全Stone格的充要条件是:对任意a,b∈L,a>b,存在有限链使得对每个i_0,x_(i-j)/x_i满足条件(S)。

In this paper we discuss the lattices with completely stonean congruence lattices.For this purpose we give the condition(S): We call the proper quotient u/v of L satisfies condition(S), if a, b, c, d∈L, a>b, c>d, a/b≈_wu/v, c/d≈_wu/v imply the existence of a proper quotient x/y satisfying x/y≈_wa / b, x/y≈_wc/d. Using the condition (S), we give the form of the atom of the skeleton S(C(L)) of the congruence lattice C(L) of L, and the characteristic of L when S(C(L)) is atomic Finally in the last section we obtain the main result of this paper: The congruence lattice C(L) of the lattice L is completely stonean if for each proper quotient a/b of L there exists a finite chain a=x_0>x_1>…>x_n=b such that each x_(i-1)/x_1 satisfies the condition (S).