An arithmetic obstruction to division algebra decomposability
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- by Eric S. Brussel PDF
- Proc. Amer. Math. Soc. 128 (2000), 2281-2285 Request permission
Abstract:
This paper presents an indecomposable finite-dimensional division algebra of $p$-power index that decomposes over a prime-to-$p$ degree field extension, obtained by adjoining $p$-th roots of unity to the base. This shows that the theory of decomposability has an arithmetic aspect.References
- E. Artin and J. Tate, Class field theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0223335
- Brussel, E.: Division algebras over Henselian fields of rank two, (in preparation).
- Nikita A. Karpenko, Torsion in $\textrm {CH}^2$ of Severi-Brauer varieties and indecomposability of generic algebras, Manuscripta Math. 88 (1995), no. 1, 109–117. MR 1348794, DOI 10.1007/BF02567809
- David J. Saltman, Finite-dimensional division algebras, Azumaya algebras, actions, and modules (Bloomington, IN, 1990) Contemp. Math., vol. 124, Amer. Math. Soc., Providence, RI, 1992, pp. 203–214. MR 1144037, DOI 10.1090/conm/124/1144037
- Jean-Pierre Serre, Local fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York-Berlin, 1979. Translated from the French by Marvin Jay Greenberg. MR 554237, DOI 10.1007/978-1-4757-5673-9
Additional Information
- Eric S. Brussel
- Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
- Email: brussel@mathcs.emory.edu
- Received by editor(s): June 10, 1998
- Received by editor(s) in revised form: October 6, 1998
- Published electronically: February 21, 2000
- Communicated by: Ken Goodearl
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2281-2285
- MSC (1991): Primary 16K20; Secondary 11R37
- DOI: https://doi.org/10.1090/S0002-9939-00-05296-5
- MathSciNet review: 1662237