Theorems · Theorem · commutative algebra

IsIntegralClosure.algebraMap_equiv

∀ (R : Type u_1) (A : Type u_2) (B : Type u_3) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : CommRing B]
  [inst_3 : Algebra R B] [inst_4 : Algebra A B] [inst_5 : IsIntegralClosure A R B] (A' : Type u_4)
  [inst_6 : CommRing A'] [inst_7 : Algebra A' B] [inst_8 : IsIntegralClosure A' R B] [inst_9 : Algebra R A]
  [inst_10 : Algebra R A'] [inst_11 : IsScalarTower R A B] [inst_12 : IsScalarTower R A' B] (x : A),
  (algebraMap A' B) ((IsIntegralClosure.equiv R A B A') x) = (algebraMap A B) x

Defined in

Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic

Cited by

5 results in Mathlib

Foundations

Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraIsIntegralClosureCommRingAlgebraIsIntegralClosureAlgebraAlgebraIsScalarTowerIsScalarTower