A Course in p-adic Analysis pp 69-126 | Cite as
Finite Extensions of the Field of p-adic Numbers
Chapter
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 .
Keywords
Haar Measure Topological Vector Space Ultrametric Analysis Quadratic Extension Residue Field
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information
© Springer Science+Business Media New York 2000