Theorems · Theorem · commutative algebra

IsFractionRing.algEquivOfAlgEquiv_algebraMap

∀ {R : Type u_8} {A : Type u_9} {K : Type u_10} {B : Type u_11} {L : Type u_12} [inst : CommSemiring R]
  [inst_1 : CommRing A] [inst_2 : CommRing B] [inst_3 : CommRing K] [inst_4 : CommRing L] [inst_5 : Algebra R A]
  [inst_6 : Algebra R K] [inst_7 : Algebra A K] [inst_8 : IsFractionRing A K] [inst_9 : IsScalarTower R A K]
  [inst_10 : Algebra R B] [inst_11 : Algebra R L] [inst_12 : Algebra B L] [inst_13 : IsFractionRing B L]
  [inst_14 : IsScalarTower R B L] (h : A ≃ₐ[R] B) (a : A),
  (IsFractionRing.algEquivOfAlgEquiv h) ((algebraMap A K) a) = (algebraMap B L) (h a)

Defined in

Mathlib.RingTheory.Localization.FractionRing

Cited by

4 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommRingCommRingCommRingCommRingAlgebraAlgebraAlgebraIsFractionRingIsScalarTowerAlgebraAlgebraAlgebraIsFractionRingIsScalarTower