Definition 8.5.19 (Tor-amplitude). Let \(R\) be a connective associative ring spectrum and let \(M\) be a left \(R\)-module. We say that \(M\) has Tor-amplitude contained in \([a,b]\) for integers \(a \leq b\) if for every discrete right \(R\)-module \(N\), the homotopy groups of \(N \otimes _R M\) are concentrated in degrees \([a,b]\), that is, \(\Tor _i^R(N,M) = 0\) whenever \(i < a\) or \(i > b\). If such \(a\) and \(b\) exist, \(M\) is said to have finite Tor-amplitude.
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