Local Field
المؤلف:
Iyanaga, S. and Kawada, Y.
المصدر:
"Local Fields." §257 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press
الجزء والصفحة:
pp. 811-815
17-10-2019
1087
Local Field
A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief applications of local field theory. A local field with field characteristic 
is isomorphic to the field of power series in one variable whose coefficients are in a finite field. A local field of characteristic zero is either 
the p-adic numbers, or power series in a complex variable.
REFERENCES:
Iyanaga, S. and Kawada, Y. (Eds.). "Local Fields." §257 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 811-815, 1980.
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