Mathematical Research Letters

Volume 15 (2008)

Number 1

A criterion for integral dependence of modules

Pages: 149 – 162



Bernd Ulrich (Purdue University)

Javid Validashti (Purdue University)


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.

Published 1 January 2008