Congruence lattices of algebras of fixed similarity type. I
Ralph S. Freese, William A. Lampe, Walter F. Taylor · Pacific Journal of Mathematics · 1979
We prove that if V is any infinite-dimensional vector space over any uncountable field F, then the congruence lattice (=subspace lattice) 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.