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Theorems · Definition · commutative algebra

HomogeneousLocalization.num

{ι : Type u_1} →
  {A : Type u_2} →
    {σ : Type u_3} →
      [inst : CommRing A] → [inst_1 : SetLike σ A] → {𝒜 : ι → σ} → {x : Submonoid A} → HomogeneousLocalization 𝒜 x → A

Numerator of an element in HomogeneousLocalization x.

Defined in
Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization
Cited by
4 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice
Assumes
CommRingSetLike
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HomogeneousLocalization.num_mem_deg · cited by 1HomogeneousLocalization.n…HomogeneousLocalization.den_smul_val · cited by 1HomogeneousLocalization.d…HomogeneousLocalization.eq_num_div_den · cited by 1HomogeneousLocalization.e…HomogeneousLocalization.Away.eventually_smul_mem · cited by 0Away.eventually_smul_memCommRing · cited by 17173CommRingSubmonoid · cited by 3086SubmonoidSetLike · cited by 1084SetLikeQuotient.out · cited by 141Quotient.outHomogeneousLocalization · cited by 69HomogeneousLocalizationHomogeneousLocalization.NumDenSameDeg.num · cited by 42NumDenSameDeg.numHomogeneousLocalization.numCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.