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Date: 3-11-2020
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Date: 17-1-2021
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Date: 12-1-2021
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Given a set of primes, a field
is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in
, and if
is the maximal set of primes split by K. Here the set
is defined up to the equivalence relation of allowing a finite number of exceptions.
The basic example is the set of primes congruent to 1 (mod 4),
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The class field for is
because every such prime is expressible as the sum of two squares
.
REFERENCES:
Cohn, H. Introduction to the Construction of Class Fields. New York: Cambridge University Press, 1985.
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