has established the rudiments of a dictionary for translating the language of projective modules into that of vector bundles. With this point of departure we have attempted to adapt some of the results and methods of homotopy theory to certain purely arithmetic and even noncommutative settings. Detailed proofs of our results will appear elsewhere. The authors are very grateful to Albrecht Dold who has educated them on the relevant parts of bundle theory.
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Bass et al. (1962) studied this question.