## A Weak Hasse Principle for Central Simple Algebras with an Involution

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2001
Lewis, David W.
Unger, Thomas
##### Publication type
Contribution to a conference collection
##### Published in
Proceedings of the Conference on Quadratic Forms and Related Topics : Baton Rouge, Louisiana, USA ; March 26 - 30, 2001 / Hoffman, J. William et al. (ed.). - Bielefeld, 2001. - (Documenta mathematica ; 2001,1). - pp. 241-251
##### Abstract
The notions of totally indefinite and weakly isotropic algebras with involution are introduced and a proof is given of the fact that a field satisfies the Effective Diagonalization Property (ED) if and only if it satisfies the following weak Hasse principle: every totally indefinite central simple algebra with involution of the first kind over the given field is weakly isotropic. This generalizes a known result from quadratic form theory.
510 Mathematics
##### Keywords
Real fields,central simple algebras,involutions,weak Hasse principles,hermitian squares
##### Conference
Quadratic Forms and Related Topics, Mar 26, 2001 - Mar 30, 2001, Baton Rouge, Louisiana, USA
##### Cite This
ISO 690LEWIS, David W., Claus SCHEIDERER, Thomas UNGER, 2001. A Weak Hasse Principle for Central Simple Algebras with an Involution. Quadratic Forms and Related Topics. Baton Rouge, Louisiana, USA, Mar 26, 2001 - Mar 30, 2001. In: HOFFMAN, J. William, ed. and others. Proceedings of the Conference on Quadratic Forms and Related Topics : Baton Rouge, Louisiana, USA ; March 26 - 30, 2001. Bielefeld, pp. 241-251
BibTex
@inproceedings{Lewis2001Hasse-23583,
year={2001},
title={A Weak Hasse Principle for Central Simple Algebras with an Involution},
number={2001,1},
series={Documenta mathematica},
booktitle={Proceedings of the Conference on Quadratic Forms and Related Topics : Baton Rouge, Louisiana, USA ; March 26 - 30, 2001},
pages={241--251},
editor={Hoffman, J. William},
author={Lewis, David W. and Scheiderer, Claus and Unger, Thomas}
}

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<dcterms:abstract xml:lang="eng">The notions of totally indefinite and weakly isotropic algebras with involution are introduced and a proof is given of the fact that a field satisfies the Effective Diagonalization Property (ED) if and only if it satisfies the following weak Hasse principle: every totally indefinite central simple algebra with involution of the first kind over the given field is weakly isotropic. This generalizes a known result from quadratic form theory.</dcterms:abstract>
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