Theorems · Inductive type · commutative algebra
IsDedekindDomainDvr
(A : Type u_1) → [inst : CommRing A] → [IsDomain A] → Prop
A Dedekind domain is an integral domain that is Noetherian, and the
localization at every nonzero prime is a discrete valuation ring.
This is equivalent to IsDedekindDomain.
- Defined in
- Mathlib.RingTheory.DedekindDomain.Dvr
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by5
Results whose statement or proof uses this declaration.
- isDedekindDomain.of_formallyUnramifiedproof · cited by 1
- isDedekindDomainDvr.of_formallyUnramifiedstatement · cited by 1
- IsDedekindDomainDvr.is_dvr_at_nonzero_primestatement and proof · cited by 1
- IsDedekindDomainDvr.casesOnstatement and proof · cited by 0
- IsDedekindDomainDvr.recOnstatement and proof · cited by 0