  Using methods developed by Franke, we obtain algebraic classification results
for modules over certain symmetric ring spectra ($S$-algebras). In particular,
for any symmetric ring spectrum $R$ whose graded homotopy ring $\pi_*R$ has
graded global homological dimension 2 and is concentrated in degrees divisible
by some natural number $N \geq 4$, we prove that the homotopy category of
$R$-modules is equivalent to the derived category of the homotopy ring
$\pi_*R$. This improves the Bousfield-Wolbert algebraic classification of
isomorphism classes of objects of the homotopy category of $R$-modules. The
main examples of ring spectra to which our result applies are the $p$-local
real connective $K$-theory spectrum $ko_{(p)}$, the Johnson-Wilson spectrum
E(2), and the truncated Brown-Peterson spectrum $BP<1>$, for an odd prime $p$.
