A single axiom for Boolean algebras (Q1800388)

Author's abtract: ``We prove that an algebra \((L,\wedge,\vee,')\) of type \((2,2,1)\) is a Boolean algebra iff \((L,\wedge,\vee)\) is a nonempty lattice that satisfies the equation \((x\wedge y)\vee(x\wedge y') =(x\vee y)\wedge(x\vee y')\).'' The proof uses the notion of weakly dicomplemented lattices, and, to prove the distributive law, uses the subdirect product of two-element lattices.