THE HEIGHT OF IDEALS AND REGULAR SEQUENCES

We prove that given a Noetherian ring R and a finitely generated N-mod ule M, there exists a finite set of prime ideals Lambda in R such that the depth or;ln arbitrary ideal I on M is determined by the height of I module each of the primes in Lambda. As an application we answer a question raised by the second author and V. Srinivas concerning m-adic approximations of regular sequences in a local ring.