A note on “small representations of finite distributive lattices as congruence lattices”

✍ Scribed by Yong Zhang

• Publisher: Springer Netherlands
• Year: 1996
• Tongue: English
• Weight: 128 KB
• Volume: 13
• Category: Article
• ISSN: 0167-8094
• DOI: 10.1007/bf00405595

✦ Synopsis

Schmidt proved that every distributive lattice with n join-irreducible elements can be represented as the congruence lattice of a "small" lattice I,, that is, a lattice L with O(r?) elements. G. Gratzer, I. Rival, and N. Zaguia proved that, for any o < 2, O(n*) can not be improved to O(rF). In this note we show that the theorem about small representation can be improved further to get a more delicate result.

Mathematics Subject Classifications (1991). Primary 06BlO; Secondary 06DOS.