Mathematical Research Letters
Volume 15 (2008)
A criterion for integral dependence of modules
Pages: 149 – 162
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.