Theorems · Theorem · commutative algebra

FractionalIdeal.count_pow

∀ {R : Type u_1} [inst : CommRing R] (K : Type u_2) [inst_1 : Field K] [inst_2 : Algebra R K]
  [inst_3 : IsFractionRing R K] [inst_4 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R) (n : ℕ)
  (I : FractionalIdeal (nonZeroDivisors R) K), FractionalIdeal.count K v (I ^ n) = ↑n * FractionalIdeal.count K v I

For every n ∈ ℕ and every ideal I, val_v(I^n) = n*val_v(I).

Defined in

Mathlib.RingTheory.DedekindDomain.Factorization

Cited by

2 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldAlgebraIsFractionRingIsDedekindDomain