Complemented congruences on complemented lattices

Melvin F. Janowitz

Vol. 73 (1977), No. 1, 87–90

DOI: 10.2140/pjm.1977.73.87

Abstract

We prove that a congruence relation on a complemented lattice has a complement if and only if it is the minimal congruence generated by a central element. This result is then used to show that a complemented lattice has a Boolean lattice of congruence relations if and only if it is the direct product of a finite number of simple lattices. It is also used to obtain some information on the structure of complemented lattices whose lattice of congruences is a Stone lattice.

Mathematical Subject Classification

Primary: 06A25, 06A25

Milestones

Received: 17 June 1976

Revised: 3 May 1977

Published: 1 November 1977