Theorems · Theorem · commutative algebra

AlgHom.map_algebraMap

∀ {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] [IsScalarTower R S A] [IsScalarTower R S B] (f : A →ₐ[S] B) (r : R),
  f ((algebraMap R A) r) = (algebraMap R B) r

Defined in

Mathlib.Algebra.Algebra.Tower

Cited by

6 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringSemiringSemiringAlgebraAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower