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

Published 9 Oct 2025 in math.AC | (2510.07779v1)

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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