Congruence amalgamation of lattices
General Mathematics
2016-08-16 v1
Abstract
J. Tuma proved an interesting "congruence amalgamation" result. We are generalizing and providing an alternate proof for it. We then provide applications of this result: --A.P. Huhn proved that every distributive algebraic lattice with at most compact elements can be represented as the congruence lattice of a lattice . We show that can be constructed as a locally finite relatively complemented lattice with zero. --We find a large class of lattices, the -congruence-finite lattices, that contains all locally finite countable lattices, in which every lattice has a relatively complemented congruence-preserving extension.
Cite
@article{arxiv.math/0501370,
title = {Congruence amalgamation of lattices},
author = {George Grätzer and Harry Lakser and Friedrich Wehrung},
journal= {arXiv preprint arXiv:math/0501370},
year = {2016}
}