semigroupSemigroup2001-10-19 11:34:322008-05-13 01:41:20Definitionsemigroup homomorphism\usepackage{amssymb}
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\usepackage{xypic}A {\em semigroup} $G$ 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 \emph{semigroup homomorphism} from $G$ to $H$ is a function $f:G\to H$ such that $f(ab)=f(a)f(b)$.