# semigroup

A $G$ is a set together with a binary operation $\cdot:G\times G\longrightarrow G$ 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