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Special forms of two symbols are division algebras

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Abstract

 If F is a valued field of characteristic p certain tensor products of cyclic F-algebras are called special forms. It is known that if F is maximally complete then every Brauer class of exponent p is represented by a special form. It is shown here that special forms of two symbols are division algebras, but that special forms of three symbols need not be, and can represent indecomposible division algebras of index $p^2$.

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Authors and Affiliations

  1. Departamento de Ciencias Físicas y Matemáticas, Universidad Arturo Prat, Casilla 121, Iquique, Chile. e-mail: raravire@cec.unap.cl. Supported by Fondecyt., , , , , , CL

    Roberto Aravire

  2. Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California, USA 93106. e-mail: jacob@math.ucsb.edu Supported by NSF and Fondecyt., , , , , , US

    Bill Jacob

Authors
  1. Roberto Aravire
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  2. Bill Jacob
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Received: 16 October 2001

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Aravire, R., Jacob, B. Special forms of two symbols are division algebras. Manuscripta Math. 108, 139–162 (2002). https://doi.org/10.1007/s002290200257

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  • DOI: https://doi.org/10.1007/s002290200257

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