POSET EMBEDDINGS OF HILBERT FUNCTIONS FOR TWO HYPERSURFACE RINGS

Let R = K[a, b, c, d]/(ad - bc) or K[a,, b, c]/(ac - b(2)), where K is a field of arbitrary characteristic and a, b, c, d are indeterminates. In this paper we will show that there is an order preserving embedding from the poset of Hilbert functions of homogeneous ideals of R to the poset of homogeneous ideals of R. We also obtain related results for Betti numbers when the characteristic of K is 0.