Reduced K0

Summary

The reduced group $\tilde{K}_0(R)$ is the quotient of $K_0(R)$ by the subgroup generated by the class of the free module $R$. It removes the part of $K_0(R)$ that only counts free modules. It vanishes exactly when every finitely generated projective module is stably free. For a Dedekind domain it is the ideal class group.