Theorems · Definition · commutative algebra

HomogeneousLocalization.Away.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) →
                  [GradedRing 𝒜] →
                    {f : A} → {d : ι} → f ∈ 𝒜 d → (n : ℕ) → (x : A) → x ∈ 𝒜 (n • d) → HomogeneousLocalization.Away 𝒜 f

This is a convenient constructor for Away 𝒜 f when f is homogeneous. Away.mk 𝒜 hf n x hx is the fraction x / f ^ n.

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

11 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRing