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 polynomial mod . Then

where are distinct prime ideals of norm . #m/thm/num/alg We also have

Corollaries

See Splitting of prime ideals in a number field.

#state/develop | #lang/en | #SemBr