Theorems · Theorem · commutative algebra

HomogeneousLocalization.map_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] {B : Type u_4} {τ : Type u_5} [inst_6 : CommRing B] [inst_7 : SetLike τ B]
  [inst_8 : AddSubgroupClass τ B] {ℬ : ι → τ} [inst_9 : GradedRing ℬ] {P : Submonoid A} {Q : Submonoid B} (g : 𝒜 →+*ᵍ ℬ)
  (comap_le : P ≤ Submonoid.comap g Q) (x : HomogeneousLocalization.NumDenSameDeg 𝒜 P),
  (HomogeneousLocalization.map g comap_le) (HomogeneousLocalization.mk x) =
    HomogeneousLocalization.mk { deg := x.deg, num := ⟨g ↑x.num, ⋯⟩, den := ⟨g ↑x.den, ⋯⟩, den_mem := ⋯ }

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRingCommRingSetLikeAddSubgroupClassGradedRing