Theorems · Theorem · commutative algebra
IsLocalRing.exists_factor_valuationRing
∀ {R : Type u_1} {K : Type u_3} [inst : CommRing R] [inst_1 : Field K] [IsLocalRing R] (f : R →+* K),
∃ A, ∃ (h : ∀ (x : R), f x ∈ A.toSubring), IsLocalHom (f.codRestrict A.toSubring h)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingFieldIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Subringstatement · cited by 602
- IsLocalRingstatement and proof · cited by 339
- ValuationSubringstatement and proof · cited by 187
- IsLocalHomstatement · cited by 100
- ValuationSubring.toSubringstatement · cited by 32
- RingHom.rangeRestrictproof · cited by 13
- Subring.inclusionproof · cited by 13
- RingHom.codRestrictstatement · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ValuativeCriterion.Existence.specializingMapproof · cited by 1