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Baer orderings with noninvariant valuation ring

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Abstract

We construct division algebras with involution containing a Baer ordering with noninvariant order ring. This gives a negative answer to a question of Holland, whether the order ring is always invariant under inner automorphisms. Furthermore, we give examples of any index. Previously, the only known examples of division algebras containing Baer orderings were of index 2n or of indexp forp a prime of the form 4m + 3.

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Author notes

  1. Patrick J. Morandi

    Present address: Department of Mathematics, New Mexico State University, Las Cruces, New Mexico, USA

Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, 78712, Austin, TX, USA

    Patrick J. Morandi

  2. Department of Mathematics, University of California, 92093, San Diego, La Jolla, CA, USA

    Adrian R. Wadsworth

Authors
  1. Patrick J. Morandi
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  2. Adrian R. Wadsworth
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Supported in part by the National Science Foundation.

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Morandi, P.J., Wadsworth, A.R. Baer orderings with noninvariant valuation ring. Israel J. Math. 68, 241–255 (1989). https://doi.org/10.1007/BF02772663

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  • DOI: https://doi.org/10.1007/BF02772663

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