Theorems · Theorem · commutative algebra

AlgEquiv.restrictScalars_apply

∀ (R : Type u) {S : Type v} {A : Type w} {B : Type u₁} [inst : CommSemiring R] [inst_1 : CommSemiring S]
  [inst_2 : Semiring A] [inst_3 : Semiring B] [inst_4 : Algebra R S] [inst_5 : Algebra S A] [inst_6 : Algebra S B]
  [inst_7 : Algebra R A] [inst_8 : Algebra R B] [inst_9 : IsScalarTower R S A] [inst_10 : IsScalarTower R S B]
  (f : A ≃ₐ[S] B) (x : A), (AlgEquiv.restrictScalars R f) x = f x

Defined in

Mathlib.Algebra.Algebra.Tower

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringSemiringSemiringAlgebraAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower