In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x <= y and a monoid xoy that admits operations x\z and z/y, loosely analogous to division or implication, when xoy is viewed as multiplication or conjunction, respectively. Called respectively right and left residuals, these operations coincide when the monoid is commutative. The general concept was introduced by Morgan Ward and Robert P. Dilworth in 1939. Examples, some of which existed prior to the general concept, include Boolean algebras, Heyting algebras, residuated Boolean algebras, relation algebras, and MV-algebras. Residuated semilattices omit the meet operation ∧, for example Kleene algebras and action algebras.