Theorems · Theorem · commutative algebra

HomogeneousIdeal.toIdeal_irrelevant_le

∀ {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] {I : Ideal A},
  (HomogeneousIdeal.irrelevant 𝒜).toIdeal ≤ I ↔ ∀ i > 0, AddSubmonoid.ofClass (𝒜 i) ≤ I.toAddSubmonoid

Defined in: Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal
Cited by: 1 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring DecidableEq AddCommMonoid PartialOrder CanonicallyOrderedAdd SetLike AddSubmonoidClass GradedRing

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Cites14

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
PartialOrderstatement and proof · cited by 6,410
Idealstatement and proof · cited by 4,748
AddSubmonoidstatement · cited by 1,178
SetLikestatement and proof · cited by 1,084
GradedRingstatement and proof · cited by 424
AddSubmonoidClassstatement and proof · cited by 346
CanonicallyOrderedAddstatement and proof · cited by 229
Submodule.toAddSubmonoidstatement · cited by 162
HomogeneousIdeal.toIdealstatement · cited by 105
HomogeneousIdeal.irrelevantstatement · cited by 46

Cited by1

Results whose statement or proof uses this declaration.

HomogeneousIdeal.irrelevant_leproof · cited by 0