A cancellative semigroup is a semigroup S = (S,·) such that
· is left cancellative: z·x = z·y ⇒ x = y and
· is right cancellative: x·z = y·z ⇒ x = y.
Let S and T be cancellative semigroups. A morphism from S to T is a function h : S→T that is a homomorphism: h(xy) = h(x)h(y).
(N, + ), the natural numbers, with additition.
|Congruence extension property|
|Definable principal congruences|
|Equationally definable principal congruences||No|
|Strong amalgamation property||No|
|Epimorphisms are surjective||No|