Tor-groups for modules

Definition 8.5.8 (Tor-groups for modules). Let \(R\) be an associative ring spectrum. For a right \(R\)-module \(M\) and a left \(R\)-module \(N\), we define the \(n\)-th Tor-group of \(M\) and \(N\) over \(R\) to be \[ \Tor ^R_n(M,N) \quad := \quad \pi _n(M \otimes _R N) \qin \Ab . \] These are the Tor-groups from Definition 6.5.6 specialized to the relative tensor product \(\RMod _R \times \LMod _R \xrightarrow {\otimes _R} \Sp \).