Theorems · Theorem · commutative algebra
HomogeneousLocalization.den_mem
∀ {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}
(f : HomogeneousLocalization 𝒜 x), f.den ∈ x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Submonoidstatement and proof · cited by 3,086
- SetLikestatement and proof · cited by 1,084
- Quotient.outproof · cited by 141
- HomogeneousLocalizationstatement and proof · cited by 69
- HomogeneousLocalization.NumDenSameDeg.den_memproof · cited by 40
- HomogeneousLocalization.denstatement · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.den_smul_valproof · cited by 1
- HomogeneousLocalization.eq_num_div_denstatement · cited by 1
- HomogeneousLocalization.Away.eventually_smul_memproof · cited by 0