Theorems · Theorem · commutative algebra

HomogeneousLocalization.awayMapAux_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 g x : A} (hx : x = f * g) (n : ι) (a : ↥(𝒜 n)) (i : ℕ) (hi : f ^ i ∈ 𝒜 n),
  (HomogeneousLocalization.awayMapAux✝ 𝒜 ⋯)
      (HomogeneousLocalization.mk { deg := n, num := a, den := ⟨f ^ i, hi⟩, den_mem := ⋯ }) =
    Localization.mk (↑a * g ^ i) ⟨x ^ i, ⋯⟩

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

2 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRing