Definition 10.58.8. Let $R$ be a local Noetherian ring and $M$ a finite $R$-module. We denote *$d(M)$* the element of $\{ -\infty , 0, 1, 2, \ldots \} $ defined as follows:

If $M = 0$ we set $d(M) = -\infty $,

if $M \not= 0$ then $d(M)$ is the degree of the numerical polynomial $\chi _ M$.

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