The Stacks project

Definition 10.59.8. 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:

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

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