Definition 15.8.3. Let $R$ be a ring. Let $M$ be a finite $R$-module. Let $k \geq 0$. The *$k$th Fitting ideal* of $M$ is the ideal $\text{Fit}_ k(M)$ constructed in Lemma 15.8.2. Set $\text{Fit}_{-1}(M) = 0$.

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