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Witt rings under odd
degree extensions
Robert Fitzgerald |
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Vol. 158 (1993), No. 1, 121–143
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Abstract |
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For a separable odd degree field extension K∕F the kernel of a Scharlau transfer of Witt rings s∗ : WK → WF is a WF-module. We compute the prime ideals attached to kers∗ and deduce that WK is not a projective WF-module if an ordering on F extends uniquely to K. An example shows WK may be a free WF-module if F is real and no ordering extends uniquely. For non-real, non-rigid F we show that K∕F Galois and WK noetherian implies WK is not a projective WF-module. |
Mathematical Subject Classification 2000
Primary: 11E81
Secondary: 12D15
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Milestones
Received: 1 December 1990
Revised: 8 July 1991
Published: 1 March 1993
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Authors |
| Robert Fitzgerald | |
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