Theorems · Theorem · commutative algebra

HomogeneousLocalization.NumDenSameDeg.map_den

∀ {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] {𝒜 : ι → σ} {B : Type u_4} {τ : Type u_5} [inst_3 : CommRing B] [inst_4 : SetLike τ B]
  [inst_5 : AddSubgroupClass τ B] {ℬ : ι → τ} (f : 𝒜 →+*ᵍ ℬ) {W₁ : Submonoid A} {W₂ : Submonoid B}
  (hw : W₁ ≤ Submonoid.comap f W₂) (c : HomogeneousLocalization.NumDenSameDeg 𝒜 W₁),
  (HomogeneousLocalization.NumDenSameDeg.map f hw c).den = (f.gradedAddHom c.deg) c.den

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingSetLikeAddSubgroupClassCommRingSetLikeAddSubgroupClass