The Hochschild cohomology ring modulo nilpotence of a monomial algebra
  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. 
E. L. Green, N. Snashall, \O. Solberg