Theorems · Theorem · commutative algebra
HomogeneousIdeal.toIdeal_irrelevant
∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : Semiring A] [inst_1 : DecidableEq ι] [inst_2 : AddCommMonoid ι]
[inst_3 : PartialOrder ι] [inst_4 : CanonicallyOrderedAdd ι] [inst_5 : SetLike σ A] [inst_6 : AddSubmonoidClass σ A]
(𝒜 : ι → σ) [inst_7 : GradedRing 𝒜],
(HomogeneousIdeal.irrelevant 𝒜).toIdeal = RingHom.ker (GradedRing.projZeroRingHom 𝒜)- Cited by
- 0 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.
Cites13
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
- AddCommMonoidstatement and proof · cited by 12,281
- RingHomstatement · cited by 10,189
- PartialOrderstatement and proof · cited by 6,410
- Idealstatement · cited by 4,748
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- RingHom.kerstatement · cited by 363
- AddSubmonoidClassstatement and proof · cited by 346
- CanonicallyOrderedAddstatement and proof · cited by 229
- HomogeneousIdeal.toIdealstatement · cited by 105
- HomogeneousIdeal.irrelevantstatement · cited by 46
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.