Theorems · Definition · commutative algebra

HomogeneousLocalization.Away.isLocalizationElem

{A : Type u_2} →
  {σ : Type u_3} →
    [inst : CommRing A] →
      [inst_1 : SetLike σ A] →
        [inst_2 : AddSubgroupClass σ A] →
          {𝒜 : ℕ → σ} →
            [GradedRing 𝒜] → {e d : ℕ} → {f : A} → f ∈ 𝒜 d → {g : A} → g ∈ 𝒜 e → HomogeneousLocalization.Away 𝒜 f

The element t := g ^ d / f ^ e such that A_{(fg)} = A_{(f)}[1/t].

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

5 results in Mathlib

Foundations

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

Assumes

CommRingSetLikeAddSubgroupClassGradedRing