English

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 DD with at most _1\aleph\_1 compact elements can be represented as the congruence lattice of a lattice LL. We show that LL can be constructed as a locally finite relatively complemented lattice with zero. --We find a large class of lattices, the ω\omega-congruence-finite lattices, that contains all locally finite countable lattices, in which every lattice has a relatively complemented congruence-preserving extension.

Keywords

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}
}
R2 v1 2026-07-22T17:14:47.460Z