The resolution of the universal ring for modules of rank zero and projective dimension two

Hochster established the existence of a commutative noetherian ring R and a universal resolution U of the form 0→Re→Rf→Rg→0 such that for any commutative noetherian ring S and any resolution V equal to 0→Se→Sf→Sg→0, there exists a unique ring homomorphism R→S with V=U⊗RS. In the present paper we assume that f=e+g and we find a resolution F of R by free P-modules, where P is a polynomial ring over the ring of integers. The resolution F is not minimal; but it is straightforward, coordinate free, and independent of characteristic. Furthermore, one can use F to calculate . If e and g both are at least 5, then is not a free abelian group; and therefore, the graded Betti numbers in the minimal resolution of by free -modules depend on the characteristic of the field . We record the modules in the minimal resolution of in terms of the modules which appear when one resolves divisors over the determinantal ring defined by the 2×2 minors of an e×g matrix.