The ordered set of principal congruences of a countable lattice
Rings and Algebras
2013-05-09 v2
Abstract
For a lattice L, let Princ L denote the ordered set of principal congruences of L. In a pioneering paper, G. Gratzer characterized the ordered sets Princ L of finite lattices L; here we do the same for countable lattices. He also showed that each bounded ordered set H is isomorphic to Princ L of a bounded lattice L. We prove a related statement: if an ordered set H with least element is the union of a chain of principal order ideals, then H is isomorphic to Princ L of some lattice L.
Keywords
Cite
@article{arxiv.1305.0965,
title = {The ordered set of principal congruences of a countable lattice},
author = {Gabor Czedli},
journal= {arXiv preprint arXiv:1305.0965},
year = {2013}
}
Comments
17 pages, 6 figures