Finite distributive lattices and doubly irreducible elements

被引：6

作者：

Berman, J

Bordalo, G

机构：

[1] UNIV ILLINOIS,DEPT MATH STAT & COMP SCI,CHICAGO,IL 60607

[2] UNIV LISBON,DEPT MATEMAT,P-1699 LISBON,PORTUGAL

来源：

DISCRETE MATHEMATICS | 1998年 / 178卷 / 1-3期

关键词：

D O I：

10.1016/S0012-365X(97)81832-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a finite ordered set G let D(G) denote the family of all distributive lattices L such that G both generates L and is the set of doubly irreducible elements of L. We provide a characterization for membership in D(G), and by means of this characterization define a natural order relation on D(G). We show that this order is a boolean lattice and we describe the maximal and minimal elements in this lattice. The maximal element is familiar: the free distributive lattice freely generated by the ordered set G. (C) 1998 Elsevier Science B.V.

引用

页码：237 / 243

页数：7