Theorems · Theorem · commutative algebra

HomogeneousLocalization.val_awayMap

∀ {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] {e : ι} {f g : A} (hg : g ∈ 𝒜 e) {x : A} (hx : x = f * g)
  (a : HomogeneousLocalization.Away 𝒜 f),
  HomogeneousLocalization.val ((HomogeneousLocalization.awayMap 𝒜 hg hx) a) =
    (Localization.awayLift (algebraMap A (Localization (Submonoid.powers x))) f ⋯) (HomogeneousLocalization.val a)

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRing