Theorems · Theorem · commutative algebra
HomogeneousIdeal.toIdeal_injective
∀ {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],
Function.Injective HomogeneousIdeal.toIdeal- Cited by
- 5 results in Mathlib
- Foundations
- Depth 95 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 · cited by 115
- HomogeneousIdeal.toIdealstatement · cited by 105
- HomogeneousSubmodule.toSubmodule_injectiveproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- HomogeneousIdeal.extproof · cited by 7
- HomogeneousIdeal.homogeneousHull_toIdeal_eq_selfproof · cited by 1
- HomogeneousIdeal.eq_bot_iffproof · cited by 0
- ProjectiveSpectrum.vanishingIdeal_iUnionproof · cited by 0
- HomogeneousIdeal.eq_top_iffproof · cited by 0