Definition 8.5.4 (Free module). Let \(R\) be an associative ring spectrum. A left \(R\)-module \(M\) is free if \(M\) is a (possibly infinite) coproduct of (unshifted) copies of \(R\), viewed as a left module over itself. A free left \(R\)-module is finitely generated if it is equivalent to a finite coproduct of copies of \(R\).
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