Congruence lattices of algebras of fixed similarity type. II
Congruence lattices of algebras of fixed similarity type. II
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 conjectureā€”that one binary operation would always ā€¦