Definition 15.65.1. Let $R$ be a ring. Let $K$ be an object of $D(R)$. We say $K$ has *finite projective dimension* if $K$ can be represented by a finite complex of projective modules. We say $K$ as *projective-amplitude in $[a, b]$* if $K$ is quasi-isomorphic to a complex

where $P^ i$ is a projective $R$-module for all $i \in \mathbf{Z}$.

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