  For a finite dimensional monomial algebra $\Lambda$ over a field $K$ we show
that the Hochschild cohomology ring of $\Lambda$ modulo the ideal generated by
homogeneous nilpotent elements is a commutative finitely generated $K$-algebra
of Krull dimension at most one. This was conjectured to be true for any finite
dimensional algebra over a field by Snashall-Solberg.
