  We show that a finite dimensional monomial algebra satisfies the finite
generation conditions of Snashall-Solberg for Hochschild cohomology if and only
if it is Gorenstein. This gives, in the case of monomial algebras, the converse
to a theorem of Erdmann-Holloway-Snashall-Solberg-Taillefer. We also give a
necessary and sufficient combinatorial criterion for finite generation.
