 Projective modules can be defined to be the direct summands of free modules.If "R" is local, any finitely generated projective module is actually free, which gives content to an analogy between projective modules and vector bundles.The Quillen–Suslin theorem asserts that any finitely generated projective module over "k"["T"1, ..., "T""n"] ("k" a field) is free, but in general these two concepts differ.