semigroup

A semigroup $G$ is a set together with a binary operation $\cdot :G\times G⟶G$ which satisfies the associative property: $(a\cdot b)\cdot c=a\cdot (b\cdot c)$ for all $a,b,c\in G$.

The set $G$ is not required to be nonempty.

Let $G,H$ be two semigroups. A semigroup homomorphism from $G$ to $H$ is a function $f:G\to H$ such that $f(ab)=f(a)f(b)$.

Title	semigroup
Canonical name	Semigroup
Date of creation	2013-03-22 11:50:08
Last modified on	2013-03-22 11:50:08
Owner	djao (24)
Last modified by	djao (24)
Numerical id	11
Author	djao (24)
Entry type	Definition
Classification	msc 20M99
Synonym	homomorphism
Related topic	groupoid
Related topic	Band2
Related topic	SubmonoidSubsemigroup
Related topic	NullSemigroup
Related topic	ZeroElements
Related topic	Monoid
Defines	semigroup homomorphism