 In more detail, an algebraic structure formula_127 is an MTL-algebra if

Important examples of MTL algebras are "standard" MTL-algebras on the real unit interval [0, 1].Further examples include all Boolean algebras, all linear Heyting algebras (both with formula_138), all MV-algebras, all BL-algebras, etc.Since the residuation condition can equivalently be expressed by identities, MTL-algebras form a variety.