Vector demetleri için Kaplansky'nin teoremi

In this master thesis, we focus on two classes of modules: The projectiveR-modules and the almost projective R-modules for a commutative ring R with unity.Then we center on the category of quasi-coherent sheaves over some special projectiveschemes and the several `new? notions of (infinite dimensional) vector bundles attainedto these classes as proposed by Drinfeld. We prove structural results relative to thedifferent generalization of vector bundles in terms of certain filtrations of locallycountably generated quasi-coherent sheaves. In the case in which the vector bundlesare built from the class of projective R-modules, our structural theorem yields a versionof Kaplansky?s Theorem for infinite dimensional vector bundles on these specialprojective schemes.