Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.exists_lift_of_le_one
∀ {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] {x : K},
(IsDedekindDomain.HeightOneSpectrum.valuation K (IsDiscreteValuationRing.maximalIdeal A)) x ≤ 1 →
∃ a, (algebraMap A K) a = x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites67
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
- Semiringproof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Unitsproof · cited by 2,804
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
Cited by2
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.mker_valuation_eq_isUnitSubmonoidproof · cited by 2
- IsDiscreteValuationRing.map_algebraMap_eq_valuationSubringproof · cited by 0