Definition 10.121.5 (02MG)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.121: Orders of vanishing
Definition 10.121.5 (cite)

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Definition 10.121.5. Let $R$ be a Noetherian local domain of dimension $1$ with fraction field $K$ . Let $V$ be a finite dimensional $K$ -vector space. Let $M$ , $M'$ be two lattices in $V$ . The distance between $M$ and $M'$ is the integer

$d(M, M') = \text{length}_ R(M/M \cap M') - \text{length}_ R(M'/M \cap M')$

of Lemma 10.121.4 part (5).

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