A Note on Congruences of Infinite Bounded Involution Lattices
Abstract
We prove that an infinite (bounded) involution lattice and even pseudoKleene algebra can have any number of congruences between $2$ and its number of elements or equalling its number of subsets, regardless of whether it has as many ideals as elements or as many ideals as subsets; consequently, the same holds for antiortholattices. Under the Generalized Continuum Hypothesis, this means that an infinite (bounded) involution lattice, pseudoKleene algebra or antiortholattice can have any number of congruences between $2$ and its number of subsets, regardless of its number of ideals.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1810.00277
 Bibcode:
 2018arXiv181000277M
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Combinatorics;
 06B10;
 06F99;
 06D30
 EPrint:
 10 pages