Theorems · Theorem · commutative algebra

FractionalIdeal.count_mul

∀ {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)
  {I I' : FractionalIdeal (nonZeroDivisors R) K},
  I ≠ 0 → I' ≠ 0 → FractionalIdeal.count K v (I * I') = FractionalIdeal.count K v I + FractionalIdeal.count K v I'

For nonzero I, I', val_v(I*I') = val_v(I) + val_v(I').

Defined in

Mathlib.RingTheory.DedekindDomain.Factorization

Cited by

4 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldAlgebraIsFractionRingIsDedekindDomain