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arXiv · 2510.07779

Note on length and multiplicity of modules over two-dimensional regular local rings

Futoshi Hayasaka·Vijay Kodiyalam
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Abstract

We give lower and upper bounds on the Buchsbaum-Rim multiplicity of finitely generated torsion-free modules over two-dimensional regular local rings, and conditions for them to attain the bounds. As consequences, we have formulae on the multiplicity of integrally closed modules.

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Futoshi Hayasaka, Vijay Kodiyalam. 2025-10-09. Note on length and multiplicity of modules over two-dimensional regular local rings. https://arxiv.org/abs/2510.07779

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