 When a vector space over a field "F" has a finite generating set, then one may extract from it a basis consisting of a finite number "n" of vectors, and the space is therefore isomorphic to "F""n".The corresponding statement with the "F" generalized to a principal ideal domain "R" is no longer true, since a basis for a finitely generated module over "R" might not exist.However such a module is still isomorphic to a quotient of some module "Rn" with "n" finite (to see this it suffices to construct the morphism that sends the elements of the canonical basis of "Rn" to the generators of the module, and take the quotient by its kernel.)