A polynomial bound on the number of comaximal localizations needed in order to make free a projective module (Q2431196)

From the author's abstract: ``Let \(\mathbf A\) be a commutative ring and \(M\) be a projective \(\mathbf A\)-module of rank \(k\) with \(n\) generators. Standard computations show that \(M\) becomes free after localizations in \(\binom nk\) comaximal elements (see Theorem 5). When the base ring \(\mathbf A\) contains a field with at least \((n-k)k+1\) non-zero distinct elements we construct a comaximal family \(G\) with at most \(((n-k)k+1)(nk+1)\) elements such that for each \(g\in G\), the module \(M_g\) is free over \(\mathcal A[1/g]\).'' Section 4 contains several interesting new questions. I am missing the Vandermonde ideal, which is mentioned in the headline of section 2.