Theorems · Theorem · commutative algebra

Ideal.ResidueField.lift_algebraMap

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] (I : Ideal R) [inst_2 : I.IsPrime]
  (f : R →+* S) (hf₁ : I ≤ RingHom.ker f) (hf₂ : I.primeCompl ≤ Submonoid.comap f (IsUnit.submonoid S)) (r : R),
  (Ideal.ResidueField.lift I f hf₁ hf₂) ((algebraMap R I.ResidueField) r) = f r

Defined in

Mathlib.RingTheory.LocalRing.ResidueField.Ideal

Cited by

2 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIdeal.IsPrime