Vol. 82, No. 1, 1979

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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
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
Authors
Ralph S. Freese
William A. Lampe
Walter Fuller Taylor