Theorems · Theorem · commutative algebra

Ideal.ResidueField.map_algebraMap

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] (I : Ideal R) [inst_2 : I.IsPrime]
  (J : Ideal S) [inst_3 : J.IsPrime] (f : R →+* S) (hf : I = Ideal.comap f J) (r : R),
  (Ideal.ResidueField.map I J f hf) ((algebraMap R I.ResidueField) r) = (algebraMap S J.ResidueField) (f r)

Defined in

Mathlib.RingTheory.LocalRing.ResidueField.Ideal

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIdeal.IsPrimeIdeal.IsPrime