Global Gorenstein dimensions of polynomial rings and of direct products   of rings
  In this paper, we extend the well-known Hilbert's syzygy theorem to the Gorenstein homological dimensions of rings. Also, we study the Gorenstein homological dimensions of direct products of rings. Our results generate examples of non-Noetherian rings of finite Gorenstein dimensions and infinite classical weak dimension. 
Driss Bennis and Najib Mahdou