Theorems · Theorem · commutative algebra

Ideal.Quotient.algEquivOfEqComap_apply

∀ {A : Type u_3} {B : Type u_4} {C : Type u_5} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : CommRing C]
  [inst_3 : Algebra A B] [inst_4 : Algebra A C] {P : Ideal B} {Q : Ideal C} (p : Ideal A) [inst_5 : Q.LiesOver p]
  [inst_6 : P.LiesOver p] {E : Type u_7} [inst_7 : EquivLike E B C] [inst_8 : AlgEquivClass E A B C] (σ : E)
  (h : P = Ideal.comap σ Q) (x : B),
  (Ideal.Quotient.algEquivOfEqComap p σ h) ((Ideal.Quotient.mk P) x) = (Ideal.Quotient.mk Q) (σ x)

Defined in

Mathlib.RingTheory.Ideal.Over

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraIdeal.LiesOverIdeal.LiesOverEquivLikeAlgEquivClass