Theorems · Theorem · field theory

RatFunc.liftAlgHom_injective

∀ {K : Type u} [inst : CommRing K] [inst_1 : IsDomain K] {L : Type u_1} {S : Type u_3} [inst_2 : Field L]
  [inst_3 : CommSemiring S] [inst_4 : Algebra S (Polynomial K)] [inst_5 : Algebra S L] (φ : Polynomial K →ₐ[S] L)
  (hφ : Function.Injective ⇑φ)
  (hφ' : optParam (nonZeroDivisors (Polynomial K) ≤ Submonoid.comap φ (nonZeroDivisors L)) ⋯),
  Function.Injective ⇑(RatFunc.liftAlgHom φ hφ')

Defined in

Mathlib.FieldTheory.RatFunc.Basic

Cited by

0 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainFieldCommSemiringAlgebraAlgebra