Congruence lattices of semilattices

Ralph S. Freese and James Bryant Nation

Vol. 49 (1973), No. 1, 51–58

DOI: 10.2140/pjm.1973.49.51

Abstract

The main result of this paper is that the class of congruence lattices of semilattices satisfies no nontrivial lattice identities. It is also shown that the class of subalgebra lattices of semilattices satisfies no nontrivial lattice identities. As a consequence it is shown that if 𝒱 is a semigroup variety all of whose congruence lattices satisfy some fixed nontrivial lattice identity, then all the members of 𝒱 are groups with exponent dividing a fixed finite number.

Mathematical Subject Classification

Primary: 06A20

Milestones

Received: 10 July 1972

Published: 1 November 1973