Some properties of projective modules over discrete Hodge algebras (Q1204544)

Let \(B\) be a discrete Hodge algebra over a Noetherian \(d\)-dimensional ring \(A\) and \(P\) a projective module over \(B\). Write \(B\) as \(R/I\), where \(I\) is generated by monomials in \(R=A[X_ 1,\ldots,X_ n]\). If either \(\text{rank} P \geq d+1\) or \(\text{rank} P\geq d\) and \(1/d! \in A\), then there exists a projective \(R\)-module \(Q\) such that \(Q/IQ \simeq P\).