Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring
∀ {A : Type u_1} {K : Type u_2} [inst : CommRing A] [inst_1 : IsDomain A] [inst_2 : IsDiscreteValuationRing A]
[inst_3 : Field K] [inst_4 : Algebra A K] [inst_5 : IsFractionRing A K],
Subring.map (algebraMap A K) ⊤ =
(IsDedekindDomain.HeightOneSpectrum.valuation K (IsDiscreteValuationRing.maximalIdeal A)).valuationSubring.toSubring- Cited by
- 0 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- Multiplicativestatement · cited by 875
- IsFractionRingstatement and proof · cited by 738
- Subringstatement · cited by 602
- WithZerostatement · cited by 586
- IsDedekindDomain.HeightOneSpectrum.valuationstatement and proof · cited by 130
Cited by1
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.equivValuationSubringproof · cited by 0