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The Whitehead group of a polynomial extension. (English) Zbl 0248.18026


MSC:

18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
19B99 Whitehead groups and \(K_1\)
16E20 Grothendieck groups, \(K\)-theory, etc.
20G35 Linear algebraic groups over adèles and other rings and schemes
55P15 Classification of homotopy type

Citations:

Zbl 0248.18025
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References:

[1] H. Bass, K-theory and Stable Algebra,Publ. math. I.H.E.S., no 22 (1964).
[2] A. Borel etJ.-P. Serre, Le théorème de Riemann-Roch (d’après Grothendieck),Bull. Soc. Math. France,86 (1959), 97–136.
[3] J. Dieudonné, Les déterminants sur un corps non-commutatif,Bull. Soc. Math. France,71 (1943), 27–45. · Zbl 0028.33904
[4] G. Higman, Units in group rings,Proc. London Math. Soc. (2),46 (1940), 231–248. · Zbl 0025.24302
[5] I. Kaplansky,Homological Dimension of Rings and Modules (mimeo. notes), University of Chicago, 1959.
[6] J.-P. Serre, Modules projectifs et espaces fibrés à fibre vectorielle,Sém. Dubreil, Paris, 1958. · Zbl 0132.41202
[7] J. H. C. Whitehead, Simple homotopy types,Amer. Jour. Math.,72 (1950), 1–57. · Zbl 0040.38901
[8] M. Atiyah andR. Bott,An elementary proof of the periodicity theorem for the complex linear group (to appear). · Zbl 0131.38201
[9] M. Atiyah andF. Hirzebruch, Vector bundles and homogeneous spaces,Proc. Sympos. Pure Math., Amer. Math. Soc., vol.3 (1961), 7–38. · Zbl 0108.17705
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