Theorems · Theorem · number theory

RingOfIntegers.dvd_norm

∀ {L : Type u_1} (K : Type u_2) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [FiniteDimensional K L]
  [IsGalois K L] (x : NumberField.RingOfIntegers L),
  x ∣ (algebraMap (NumberField.RingOfIntegers K) (NumberField.RingOfIntegers L)) ((RingOfIntegers.norm K) x)

If L/K is a finite Galois extension of fields, then, for all (x : 𝓞 L) we have that x ∣ algebraMap (𝓞 K) (𝓞 L) (norm K x).

Defined in

Mathlib.NumberTheory.NumberField.Norm

Cited by

1 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFiniteDimensionalIsGalois