The following variant of this is also used: instead of finitely generated projective (= locally free) modules, take finitely generated modules. The resulting "K"-groups are usually written "G""n"("R"). When "R" is a noetherian regular ring, then "G"- and "K"-theory coincide. Indeed, the global dimension of regular rings is finite, i.e. any finitely generated module has a finite projective resolution "P"* → "M", and a simple argument shows that the canonical map "K"0(R) → "G"0(R) is an isomorphism, with ["M"]=Σ ± ["P""n"]. This isomorphism extends to the higher "K"-groups, too.