Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

On complete d-sequences and the defining ideals of Rees algebras

Sam Huckabaa1

a1 Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, U.S.A.


If R is a Noetherian local ring and I = (x1, …, xn)R is an ideal of R then the Rees algebra R[It] can be represented as a homomorphic image of the polynomial ring R[Z1, …, Zn]. The kernel is a homogeneous ideal, and the smallest of the degree bounds among all generating sets, called the relation type of I, is independent of the representation. We derive formulae connecting the relation type of I with the reduction number of I when the analytic spread of I exceeds height(I) by one. In the process we define complete d-sequences with respect to I and use them to help achieve our results. In addition some results on the behaviour of the relation type modulo an element are proved, and examples where the relation type is explicitly computed are presented.

(Received December 06 1988)