Theorems · Definition · commutative algebra

HomogeneousLocalization.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} →
                        g ∈ 𝒜 e →
                          {x : A} → x = f * g → HomogeneousLocalization.Away 𝒜 f →+* HomogeneousLocalization.Away 𝒜 x

Given x = f * g with g homogeneous of positive degree, this is the map A_{(f)} → A_{(x)} taking a/f^i to ag^i/(fg)^i.

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

27 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRing