This analysis explores bounds on multiplicity and conditions for modules over two-dimensional local rings, suggesting implications for integrally closed modules.
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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Hayasaka et al. (2026) studied this question.
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