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Wedderburn's factorization theorem application to reduced  -theory
Author(s):
R.
Hazrat
Journal:
Proc. Amer. Math. Soc.
130
(2002),
311-314.
MSC (2000):
Primary 16A39
Posted:
May 25, 2001
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Abstract:
This article provides a short and elementary proof of the key theorem of reduced  -theory, namely Platonov's Congruence theorem. Our proof is based on Wedderburn's factorization theorem.
References:
-
- 1.
- P. Draxl, Skew Field, London Math. Soc. Lecture Note Ser. Vol 81, Cambridge, Univ. Press. Cambridge, 1983. MR 85a:16022
- 2.
- P. Draxl, M. Kneser (eds.),
 von Schiefkörpern, Lecture Notes in Math. Vol 778, Springer, Berlin, 1980. MR 82b:16014 - 3.
- Y. Ershov, Henselian valuation of division rings and the group
 , Math USSR Sb. 45 (1983), 63-71. - 4.
- R. Hazrat,
 -like functors for division algebras, J. of Algebra, to appear. - 5.
- V. P. Platonov, The Tannaka-Artin problem and reduced
 -theory, Math USSR Izv. 10 (1976), 211-243. - 6.
- V. P. Platonov, V. Yanchevskii, Algebra IX, Finite dimensional division algebras, Encyclopaedia Math. Sci. 77, Springer, Berlin, 1995.
- 7.
- I. Reiner, Maximal Orders, Academic Press, London, 1975. MR 52:13910
- 8.
- L. Rowen, Y. Segev, The multiplicative group of a division algebra of degree 5 and Wedderburn's factorization theorem, Contemp. Math., 259, Amer. Math. Soc., 2000. CMP 2001:01
- 9.
- A. Suslin,
 of division algebras and Galois cohomology, Advances in Soviet Math 4, Amer. Math. Soc. (1991), 75-99. - 10.
- J.-P. Tignol, A. R. Wadsworth, Totally ramified valuations on finite-dimensional division algebras, Tran. Amer. Math. Soc. 302 (1) (1987), 223-250. MR 88j:16025
- 11.
- A. R. Wadsworth, Extending valuations to finite dimensional division algebras, Proc. Amer. Math. Soc. 98 (1986), 20-22. MR 87i:16025
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Additional Information:
R.
Hazrat
Affiliation:
Department of Mathematics, University of Bielefeld, P. O. Box 100131, 33501 Bielefeld, Germany
Email:
rhazrat@mathematik.uni-bielefeld.de
DOI:
10.1090/S0002-9939-01-06083-X
PII:
S 0002-9939(01)06083-X
Keywords:
Division algebra,
reduced $K$-theory,
congruence theorem,
reduced Whitehead group
Received by editor(s):
April 13, 2000
Received by editor(s) in revised form:
June 12, 2000
Posted:
May 25, 2001
Communicated by:
Lance W. Small
Copyright of article:
Copyright
2001,
American Mathematical Society
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