A generalization of an inequality of Lech relating multiplicity and\n colength

2017/11/18 by Craig Huneke, Huneke, Craig, Ilya Smirnov +3
Engineering · Mathematics · #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1711.06951

openalex publication_date 2017/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study conjectured generalizations of a formula of Lech which relates the\nmultiplicity of a finite colength ideal in an equicharacteristic local ring to\nits colength, and prove one of these generalizations involving the multiplicity\nof the maximal ideal times the finite colength ideal. We also propose a\nLech-type formula that relates multiplicity and the number of generators. We\nprove the conjecture in dimension three and establish a weaker result in full\ngenerality.\n

Related

• Asymptotic Lech's inequality
• Colength, multiplicity, and ideal closure operations II
• The multiplicity and the number of generators of an integrally closed ideal
• Lech's Inequality for the Buchsbaum-Rim Multiplicity and Mixed Multiplicity
• Strongly Lech-independent ideals and Lech's conjecture