Definition 15.69.1. Let $R$ be a ring. Let $K$ be an object of $D(R)$. We say $K$ has finite injective dimension if $K$ can be represented by a finite complex of injective $R$-modules. We say $K$ has injective-amplitude in $[a, b]$ if $K$ is isomorphic to a complex

$\ldots \to 0 \to I^ a \to I^{a + 1} \to \ldots \to I^{b - 1} \to I^ b \to 0 \to \ldots$

with $I^ i$ an injective $R$-module for all $i \in \mathbf{Z}$.

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