  If $R$ is a finite commutative ring, then the affine monoid of $R$ is the
monoid of all affine mappings $x\mapsto ax+b$ on $R$. Alternatively, it is the
semidirect product of the multiplicative monoid of $R$ with the additive group
of $R$. In this paper we compute the Gabriel quiver of the complex algebra of
the affine monoid of any finite commutative ring.
