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The existence of
natural field structures for finite dimensional vector spaces
over local fields
Mitchell Herbert Taibleson |
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Vol. 63 (1976), No. 2, 545–551
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Abstract |
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Let K be a local field (e.g., a p-adic or p-series field) and n a positive integer. Let K′ be the unique (up to isomorphism) unramified extension of K. It is shown that the natural (modular) norm of K′ is the n-th power of the usual (l∞) vector space norm of K′ when K′ is viewed as an n-dimensional vector space over K. Further, the two distinct descriptions of the dual of K′ (which is isomorphic to K′) that arise from the field model and vector space model are isomorphic under a K-linear isomorphism of K′ as a vector space over K, and the isomorphism is norm preserving. |
Mathematical Subject Classification 2000
Primary: 12B40, 12B40
Secondary: 43A70
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Milestones
Received: 7 August 1975
Published: 1 April 1976
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Authors |
| Mitchell Herbert Taibleson | |
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