A cancellative commutative monoid is a cancellative monoid M = (M,·,e) such that · is commutative: x·y = y·x.
Let M and N be cancellative commutative monoids. A morphism from M to N is a function h : M→N that is a homomorphism: h(x·y) = h(x)·h(y) and h(e) = e.
All commutative free monoids are cancellative.
All finite commutative (left or right) cancellative monoids are reducts of abelian groups.
(N, + ,0), the natural numbers, with addition and zero.
|Congruence extension property|
|Definable principal congruences|
|Equationally definable principal congruences|
|Strong amalgamation property|
|Epimorphisms are surjective|