Theorems · Theorem · commutative algebra
HomogeneousIdeal.ext
∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : Semiring A] [inst_1 : SetLike σ A]
[inst_2 : AddSubmonoidClass σ A] {𝒜 : ι → σ} [inst_3 : DecidableEq ι] [inst_4 : AddMonoid ι] [inst_5 : GradedRing 𝒜]
{I J : HomogeneousIdeal 𝒜}, I.toIdeal = J.toIdeal → I = J- Cited by
- 7 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Idealstatement · cited by 4,748
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- HomogeneousIdealstatement and proof · cited by 115
- HomogeneousIdeal.toIdealstatement and proof · cited by 105
- HomogeneousIdeal.toIdeal_injectiveproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- HomogeneousIdeal.toIdeal_homogeneousCore_eq_selfproof · cited by 1
- HomogeneousIdeal.map_mapproof · cited by 1
- ProjectiveSpectrum.vanishingIdeal_closureproof · cited by 0
- ProjectiveSpectrum.vanishingIdeal_unionproof · cited by 0
- Ideal.homogeneousHull_eq_iSupproof · cited by 0
- HomogeneousIdeal.ext_iffproof · cited by 0
- HomogeneousIdeal.map_idproof · cited by 0