AUT Journal of Mathematics and Computing

AUT Journal of Mathematics and Computing

A proof for a general form of the Serre-Swan theorem

Document Type : Short Contribution

Authors
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
Abstract
In this brief note, we present a proof for a general form of the Serre-Swan theorem.
Keywords
Subjects

[1] J. Dixmier, C-algebras, North-Holland Mathematical Library, Vol. 15, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Translated from the French by Francis Jellett.
[2] G. B. Folland, Real analysis – Modern techniques and their applications, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, second ed., 1999.
[3] C. Heunen and M. L. Reyes, Frobenius structures over Hilbert C-modules, Comm. Math. Phys., 361 (2018), pp. 787–824.
[4] K. H. Hofmann, Representations of algebras by continuous sections, Bull. Amer. Math. Soc., 78 (1972), pp. 291– 373.
[5] H. Li, A Hilbert C-module admitting no frames, Bull. Lond. Math. Soc., 42 (2010), pp. 388394.
[6] R. G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc., 105 (1962), pp. 264–277.
[7] A. Takahashi, Hilbert modules and their representation, Rev. Colombiana Mat., 13 (1979), pp. 1–38.