Theorems · Theorem · commutative algebra

IsFractionRing.fieldEquivOfAlgEquivHom_injective

∀ (A : Type u_8) (B : Type u_9) [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] (K : Type u_10)
  (L : Type u_11) [inst_3 : Field K] [inst_4 : Field L] [inst_5 : Algebra A K] [inst_6 : Algebra B L]
  [inst_7 : IsFractionRing A K] [inst_8 : IsFractionRing B L] [inst_9 : Algebra A L] [inst_10 : IsScalarTower A B L]
  [inst_11 : Algebra K L] [inst_12 : IsScalarTower A K L],
  Function.Injective ⇑(IsFractionRing.fieldEquivOfAlgEquivHom K L)

Defined in

Mathlib.RingTheory.Localization.FractionRing

Cited by

2 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFieldFieldAlgebraAlgebraIsFractionRingIsFractionRingAlgebraIsScalarTowerAlgebraIsScalarTower