Mathematical Research Letters

Volume 15, Issue 1, January 2008 pp. 149-162.

A criterion for integral dependence of modules

Authors: Bernd Ulrich (1) and Javid Validashti (2)
Author institution: Purdue University (1) and Purdue University (2)

Summary: 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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