Theorems · Theorem · commutative algebra
Associates.finprod_ne_zero
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (I : Ideal R),
Associates.mk (∏ᶠ (v : IsDedekindDomain.HeightOneSpectrum R), v.maxPowDividing I) ≠ 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 149 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.
Cites19
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
- one_ne_zeroproof · cited by 885
- IsDedekindDomainstatement and proof · cited by 668
- Set.Finite.toFinsetproof · cited by 351
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- finprodstatement · cited by 257
- Associatesstatement · cited by 210
- pow_ne_zeroproof · cited by 208
- IsDedekindDomain.HeightOneSpectrum.asIdealproof · cited by 156
- Associates.mkstatement and proof · cited by 137
- Function.HasFiniteMulSupportproof · cited by 99
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.finprod_heightOneSpectrum_factorizationproof · cited by 6
- Ideal.finprod_countproof · cited by 1