Theorems · Theorem · commutative algebra
HomogeneousIdeal.eq_top_iff
∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : Semiring A] [inst_1 : DecidableEq ι] [inst_2 : AddMonoid ι]
[inst_3 : SetLike σ A] [inst_4 : AddSubmonoidClass σ A] {𝒜 : ι → σ} [inst_5 : GradedRing 𝒜] (I : HomogeneousIdeal 𝒜),
I = ⊤ ↔ I.toIdeal = ⊤- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Top.topstatement · cited by 9,680
- 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 · cited by 105
- HomogeneousIdeal.toIdeal_injectiveproof · cited by 5
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