Theorems · Theorem · commutative algebra

IsIntegralClosure.algebraMap_lift

∀ (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] {S : Type u_4} [inst_6 : CommRing S]
  [inst_7 : Algebra R S] [inst_8 : Algebra S B] [inst_9 : IsScalarTower R S B] [inst_10 : Algebra R A]
  [inst_11 : IsScalarTower R A B] [isIntegral : Algebra.IsIntegral R S] (x : S),
  (algebraMap A B) ((IsIntegralClosure.lift R A B) x) = (algebraMap S B) x

Defined in

Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic

Cited by

3 results in Mathlib

Foundations

Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraIsIntegralClosureCommRingAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerAlgebra.IsIntegral