Splitting of prime ideals in a number field

Kummer’s factorization theorem

Let be a number field where is an algebraic integer, and suppose is a prime number not dividing the annoying index . Let be the minimal polynomial of , and write

for ^irreducible mod . Then

where are distinct prime ideals of norm . alg We also have

Proof

proof

Corollaries

See Splitting of prime ideals in a number field.

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