Abstract
The field Q p is not algebraically closed: It admits algebraic extensions of arbitrarily large degrees. These extensions are the p-adic fields to be studied here. Each one is a finite-dimensional, hence locally compact, normed space over Q p . A main result is the following: The p-adic absolute value on Q p has a unique extension to any finite algebraic extension K of Q p .
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© 2000 Springer Science+Business Media New York
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Robert, A.M. (2000). Finite Extensions of the Field of p-adic Numbers. In: A Course in p-adic Analysis. Graduate Texts in Mathematics, vol 198. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3254-2_2
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DOI: https://doi.org/10.1007/978-1-4757-3254-2_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3150-4
Online ISBN: 978-1-4757-3254-2
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