Theorems · Theorem · commutative algebra
IsDedekindDomainDvr.is_dvr_at_nonzero_prime
∀ {A : Type u_1} {inst : CommRing A} {inst_1 : IsDomain A} [self : IsDedekindDomainDvr A] (P : Ideal A),
P ≠ ⊥ → ∀ (x : P.IsPrime), IsDiscreteValuationRing (Localization.AtPrime P)- Defined in
- Mathlib.RingTheory.DedekindDomain.Dvr
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsDedekindDomainDvr
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 4,748
- Bot.botstatement · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- Ideal.IsPrimestatement · cited by 827
- Ideal.primeComplstatement · cited by 462
- Localization.AtPrimestatement · cited by 299
- IsDiscreteValuationRingstatement · cited by 117
- IsDedekindDomainDvrstatement and proof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.trace_quotient_eq_of_isDedekindDomainproof · cited by 3