Theorems · Theorem · commutative algebra
IsFractionRing.isFractionRing_of_isDomain_of_isLocalization
∀ {R : Type u_1} [inst : CommRing R] (M : Submonoid R) [IsDomain R] (S : Type u_2) (T : Type u_3) [inst_2 : CommRing S]
[inst_3 : CommRing T] [inst_4 : Algebra R S] [inst_5 : Algebra R T] [inst_6 : Algebra S T] [IsScalarTower R S T]
[IsLocalization M S] [IsFractionRing R T], IsFractionRing S T- Cited by
- 6 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- mul_oneproof · cited by 3,885
- Submonoidstatement and proof · cited by 3,086
- Nontrivialproof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- IsFractionRingstatement and proof · cited by 738
- IsLocalizationstatement and proof · cited by 636
- zero_ne_oneproof · cited by 90
- RingHom.map_oneproof · cited by 76
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.spanIntNorm_localizationproof · cited by 3
- Algebra.intNorm_eq_of_isLocalizationproof · cited by 1
- IsLocalization.isDedekindDomainproof · cited by 1
- isIntegrallyClosed_of_isLocalizationproof · cited by 1
- Algebra.intTrace_eq_of_isLocalizationproof · cited by 1
- FractionRing.isSeparable_of_isLocalizationproof · cited by 0