Theorems · Theorem · commutative algebra
Ideal.finprod_heightOneSpectrum_pow_multiplicity
∀ {R : Type u_3} [inst : CommRing R] [IsDedekindDomain R] {I : Ideal R},
I ≠ ⊥ → ∏ᶠ (p : IsDedekindDomain.HeightOneSpectrum R), p.asIdeal ^ multiplicity p.asIdeal I = I- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDedekindDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- finprodstatement and proof · cited by 257
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement · cited by 156
- multiplicitystatement · cited by 117
- Ideal.finprod_heightOneSpectrum_factorizationproof · cited by 6
- IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiplicityproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.FinitePlace.finprod_finitePlace_pow_multiplicityproof · cited by 0