Theorems · Theorem · commutative algebra

Algebra.Generators.Hom.algebraMap_toAlgHom

∀ {R : Type u} {S : Type v} {ι : Type w} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  {P : Algebra.Generators R S ι} {R' : Type u_1} {S' : Type u_2} {ι' : Type u_3} [inst_3 : CommRing R']
  [inst_4 : CommRing S'] [inst_5 : Algebra R' S'] {P' : Algebra.Generators R' S' ι'} [inst_6 : Algebra R R']
  [inst_7 : Algebra S S'] [inst_8 : Algebra R S'] [IsScalarTower R R' S'] [IsScalarTower R S S'] (f : P.Hom P')
  (x : P.Ring), (MvPolynomial.aeval P'.val) (f.toAlgHom x) = (algebraMap S S') ((MvPolynomial.aeval P.val) x)

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

6 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower