Theorems · Theorem · commutative algebra

Algebra.Generators.Hom.toAlgHom_monomial

∀ {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'] (f : P.Hom P') (v : ι →₀ ℕ) (r : R),
  f.toAlgHom ((MvPolynomial.monomial v) r) = r • v.prod fun x1 x2 => f.val x1 ^ x2

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

2 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebra