Theorems · Theorem · commutative algebra

HomogeneousLocalization.Away.val_mk

∀ {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] {f : A} {d : ι} (n : ℕ) (hf : f ∈ 𝒜 d) (x : A) (hx : x ∈ 𝒜 (n • d)),
  HomogeneousLocalization.val (HomogeneousLocalization.Away.mk 𝒜 hf n x hx) = Localization.mk x ⟨f ^ n, ⋯⟩

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

0 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRing