Theorems · Theorem · commutative algebra
HomogeneousLocalization.val_zero
∀ {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] {x : Submonoid A}, HomogeneousLocalization.val 0 = 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- AddCommMonoidstatement and proof · cited by 12,281
- Submonoidstatement and proof · cited by 3,086
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- Localizationstatement · cited by 270
- AddSubgroupClassstatement and proof · cited by 240
- HomogeneousLocalizationstatement · cited by 69
- HomogeneousLocalization.valstatement · cited by 51
- HomogeneousLocalization.NumDenSameDeg.denproof · cited by 47
- HomogeneousLocalization.NumDenSameDeg.den_memproof · cited by 40
- Localization.mk_zeroproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.zero_memproof · cited by 2
- HomogeneousLocalization.val_natCastproof · cited by 1
- HomogeneousLocalization.Away.span_mk_prod_pow_eq_topproof · cited by 1
- HomogeneousLocalization.mk_eq_zero_of_numproof · cited by 0
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.primeproof · cited by 0