A commutative residuated lattice is a residuated lattice L = (L,∨,∧,·,e,\,/) such that
· is commutative: xy = yx.
Let L and M be commutative residuated lattices. A morphism from L to M is a function h : L→M that is a homomorphism: h(x∨y) = h(x)∨h(y) and h(x∧y) = h(x)∧h(y) and h(x·y) = h(x)·h(y) and h(x\y) = h(x)\h(y) and h(x/y) = h(x)/h(y) and h(e) = e.
|Congruence n-permutable||Yes, n=2|
|Congruence extension property||Yes|
|Definable principal congruences||No|
|Equationally definable principal congruences||No|
|Strong amalgamation property|
|Epimorphisms are surjective|