Theorems · Theorem · commutative algebra

Algebra.Generators.Hom.equivAlgHom_symm_apply_val

∀ {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'] [inst_9 : IsScalarTower R R' S'] [inst_10 : IsScalarTower R S S']
  (f : { f // ∀ (x : P.Ring), (MvPolynomial.aeval P'.val) (f x) = (algebraMap S S') ((MvPolynomial.aeval P.val) x) })
  (i : ι), (Algebra.Generators.Hom.equivAlgHom.symm f).val i = ↑f (MvPolynomial.X i)

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

0 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower