Baer orderings with noninvariant valuation ring |
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| Authors: | Patrick J. Morandi Adrian R. Wadsworth |
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| Affiliation: | (1) Department of Mathematics, The University of Texas at Austin, 78712 Austin, TX, USA;(2) Department of Mathematics, University of California, 92093 San Diego, La Jolla, CA, USA;(3) Present address: Department of Mathematics, New Mexico State University, Las Cruces, New Mexico, USA |
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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 2 n or of indexp forp a prime of the form 4m + 3. Supported in part by the National Science Foundation. |
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