Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Wedderburn's factorization theorem application to reduced $K$-theory


Author: R. Hazrat
Journal: Proc. Amer. Math. Soc. 130 (2002), 311-314
MSC (2000): Primary 16A39
DOI: https://doi.org/10.1090/S0002-9939-01-06083-X
Published electronically: May 25, 2001
MathSciNet review: 1862107
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

This article provides a short and elementary proof of the key theorem of reduced $K$-theory, namely Platonov's Congruence theorem. Our proof is based on Wedderburn's factorization theorem.


References [Enhancements On Off] (What's this?)

  • 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.), $SK_{1}$ 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 $SK_{1}(D)$, Math USSR Sb. 45 (1983), 63-71.
  • 4. R. Hazrat, $SK_{1}$-like functors for division algebras, J. of Algebra, to appear.
  • 5. V. P. Platonov, The Tannaka-Artin problem and reduced $K$-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, $SK_{1}$ 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16A39

Retrieve articles in all journals with MSC (2000): 16A39


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: https://doi.org/10.1090/S0002-9939-01-06083-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
Published electronically: May 25, 2001
Communicated by: Lance W. Small
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society