Congruence lattices of algebras of fixed similarity type. I

Ralph S. Freese, William A. Lampe and Walter Fuller Taylor

Vol. 82 (1979), No. 1, 59–68

DOI: 10.2140/pjm.1979.82.59

Abstract

We prove that if V is any infinite-dimensional vector space over any uncountable field F, then the congruence Iattice (=subspace Iattice) of V cannot be represented as a congruence lattice (of any algebra) without using at least |F| operations. This refutes a long-standing conjecture—that one binary operation would always suffice.

Mathematical Subject Classification 2000

Primary: 08A30

Milestones

Received: 7 June 1978

Published: 1 May 1979