Projective dimension of the universal modules for the product of a hypersurface and affine T-space

The main result in this paper is that the projective dimension of the nth o rder universal module of the coordinate ring of the product of a reduced hy persurface and an affine t-space is finite. This question appears in [1]. W e have seen this by showing that projective dimension of the nth order univ ersal module of the ring corresponding to a reduced hypersurface is finite. At the end we present some examples related to projective dimension of the universal modules of the product of variaties.