Lemma 43.15.2. Let $A$ be a Noetherian local ring. Let $I \subset A$ be an ideal of definition. Let $0 \to M' \to M \to M'' \to 0$ be a short exact sequence of finite $A$-modules. Let $d \geq \dim (\text{Supp}(M))$. Then

$e_ I(M, d) = e_ I(M', d) + e_ I(M'', d)$

Proof. Immediate from the definitions and Algebra, Lemma 10.59.10. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).