One of the aims of this paper is to answer the following question: Let R be a commutative ring for which projective ideals are finitely generated; is the same valid in R [x], the polynomial ring in one variable over R? A Hilbert basis type of argument does not seem to lead directly to a solution. Instead we were taken to consider a special case of the following problem: Let (X, Ox) be a prescheme and M a quasi-coherent Ox-module with finitely generated stalks; when is M of finite type? Examples abound where this is not so and here it is shown that a ring for which a projective module with finitely generated localizations is always finitely generated, is precisely one of the kind mentioned above (Theorem 2.1). Such a ring R could also be characterized as "any finitely generated flat module is projective."