Theorems · Theorem · commutative algebra
Valuation.Integers.isFractionRing
∀ {𝒪 : Type u} {K : Type v} {Γ : Type w} [inst : CommRing 𝒪] [inst_1 : Field K] [inst_2 : Algebra 𝒪 K]
[inst_3 : LinearOrderedCommGroupWithZero Γ] {v : Valuation K Γ}, v.Integers 𝒪 → IsFractionRing 𝒪 K- Cited by
- 1 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Valuationstatement and proof · cited by 823
- IsFractionRingstatement · cited by 738
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.Integersstatement and proof · cited by 58
- Valuation.Integers.hom_injproof · cited by 14
- isFractionRing_of_exists_eq_algebraMap_or_inv_eq_algebraMap_of_injectiveproof · cited by 2
- Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMapproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.Integers.isIntegrallyClosedproof · cited by 0