A commutative semigroup is a semigroup S = (S,·) such that · is commutative: xy = yx.
A commutative semigroup is a structure S = (S,·), where · is an infix binary operation, called
the semigroup product, such that
· is associative: (xy)z = x(yz)and
· is commutative: xy = yx.
Let S and T be commutative 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.
|Equational theory||decidable in polynomial time|
|Congruence extension property|
|Definable principal congruences|
|Equationally definable principal congruences||no|
|Strong amalgamation property||no|
|Epimorphisms are surjective||no|
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