Abstract
Let (R, 𝔪) be a Noetherian local ring and M be a submodule of the free module F = R r with height(I r (M)) > 0. Asymptotic sequences over M will be defined analogous to Rees’ definition of asymptotic sequences over an ideal. It is then shown that all maximal asymptotic sequences over M have the same length. This length gives a bound on the analytic spread of M. Namely, if s is the length of a maximal asymptotic sequence over M then l(M) ≤dim R + rank M − 1 − s. Equality holds if R is quasi-unmixed.
2000 Mathematics Subject Classification:
Notes
Communicated by I. Swanson.