Theorems · Theorem · commutative algebra

HomogeneousLocalization.val_localRingHom

∀ {ι : Type u_1} {A : Type u_2} {σ : Type u_3} [inst : CommRing A] [inst_1 : SetLike σ A]
  [inst_2 : AddSubgroupClass σ A] [inst_3 : AddCommMonoid ι] [inst_4 : DecidableEq ι] {𝒜 : ι → σ}
  [inst_5 : GradedRing 𝒜] {B : Type u_4} {τ : Type u_5} [inst_6 : CommRing B] [inst_7 : SetLike τ B]
  [inst_8 : AddSubgroupClass τ B] {ℬ : ι → τ} [inst_9 : GradedRing ℬ] {f : 𝒜 →+*ᵍ ℬ} {I : Ideal A} [inst_10 : I.IsPrime]
  {J : Ideal B} [inst_11 : J.IsPrime] {hIJ : I = Ideal.comap f J} (x : HomogeneousLocalization.AtPrime 𝒜 I),
  HomogeneousLocalization.val ((HomogeneousLocalization.localRingHom f I J hIJ) x) =
    (Localization.localRingHom I J (↑f) hIJ) (HomogeneousLocalization.val x)

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

2 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRingCommRingSetLikeAddSubgroupClassGradedRingIdeal.IsPrimeIdeal.IsPrime