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Original Articles

On the Vasconcelos inequality for the fiber multiplicity of modules

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Pages 3322-3333 | Received 22 Jun 2017, Published online: 17 Jan 2018
 

ABSTRACT

Let (R,𝔪) be a Noetherian local ring of dimension d>0 with infinite residue field. Let M be a finitely generated proper R-submodule of a free R-module F with (FM)<∞ and having rank r. In this article, we study the fiber multiplicity f0(M) of the module M. We prove that if (R,𝔪) is a two-dimensional Cohen–Macaulay local ring, then f0(M)br1(M)br0(M)+(FM)+μ(M)r, where bri(M) denotes the ith Buchsbaum-Rim coefficient of M.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgments

We sincerely thank the referees for pointing out several errors, some of them typographical and some of them mathematical, which tremendously improved the exposition.

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