Mathematical Research Letters

Volume 15 (2008)

Number 1

A criterion for integral dependence of modules

Pages: 149 – 162

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n1.a13

Authors

Bernd Ulrich (Purdue University)

Javid Validashti (Purdue University)

Abstract

Let $R$ be a universally catenary locally equidimensional Noetherian ring. We give a multiplicity based criterion for an arbitrary finitely generated $R$-module to be integral over a submodule. Our proof is self-contained and implies the previously known numerical criteria for integral dependence of ideals and modules.

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