A Lower Bound for Congruence Representations |
| |
Authors: | George Grätzer Dabin Wang |
| |
Institution: | (1) Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada |
| |
Abstract: | G. Grätzer, H. Lakser, and E. T. Schmidt proved that every finite distributive lattice D with n join-irreducible elements can be represented as the congruence lattice of a lattice L with O(n2) elements. G. Grätzer, I. Rival, and N. Zaguia gave kn, < 2, as a lower bound for the size of such a lattice L; a sharper form, 1/64(n/log2n)2, of this result was given by Y. Zhang.In this note, we apply a recent result of R. Freese, to obtain 1/16 n2/log2n as a lower bound. We also give a direct proof of Freese's result. |
| |
Keywords: | lattice congruence lattice distributive projectivity join-irreducible |
本文献已被 SpringerLink 等数据库收录! |
|