Abstract
It is fairly easy to see that any rank 1 f.g. projective module over k[t1, ..., t n ] (k a field) is free. To give a proof of this, we start with the following characterization of rank 1 projective modules over any (commutative) integral domain.
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References
See, e.g. [Nagata: 1962], p. 26.
In the literature, Grothendieck’s Theorem (5.8) is sometimes attributed to both Grothendieck and Serre; see, e.g. [Swan: 1975], p. 6.
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© 2006 Springer-Verlag Berlin Heidelberg
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Lam, T.Y. (2006). The “Classical” Results on Serre’s Conjecture. In: Serre’s Problem on Projective Modules. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34575-6_3
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DOI: https://doi.org/10.1007/978-3-540-34575-6_3
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