Example 6.7.5. Let \(R\) be a PID and let \(A, B \in \D ^-(R)\). If all homology groups \(H_i(A)\) are flat (equivalently, torsion-free), then \[ H_n(A \otimes ^{\bL }_R B) \;\cong \; \bigoplus _{i+j=n} H_i(A) \otimes _R H_j(B). \]
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