Commutative semigroups

Abbreviation: CSgrp

Definition

A commutative semigroup is a semigroup S = (S,·) such that · is commutative:   xy = yx.

Definition

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.

Morphisms

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).

Some results

Examples

(N, + ), the natural numbers, with additition.

Properties

Finite members

Size 1:  1
Size 2:  3
Size 3:  12
Size 4:  58
Size 5:  325
[Size 6]?:  2143
[Size 7]?:  17291

Subclasses

Superclasses