A non-Archimedean local field is a field that is complete with respect to a nontrivial discrete non-Archimedean
valuation and has a finite residue field. Examples
include finite extensions of the p-adic numbers
and the formal Laurent series 
over a finite field.
Non-Archimedean Local Field
See also
Local Field, Non-Archimedean Valuation, Residue Characteristic, Residue FieldExplore with Wolfram|Alpha
References
Serre, J.-P. Local Fields. New York: Springer-Verlag, 1979.Cite this as:
Weisstein, Eric W. "Non-Archimedean Local Field." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Non-ArchimedeanLocalField.html