Theorems · Definition · commutative algebra

HomogeneousLocalization.mapId

{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] →
                    {P Q : Submonoid A} → P ≤ Q → HomogeneousLocalization 𝒜 P →+* HomogeneousLocalization 𝒜 Q

Let A be a graded ring and P ≤ Q be two submonoids, then the homogeneous localization of A at P embeds into the homogeneous localization of A at Q.

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

7 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRing