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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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