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Theorems · Theorem · commutative algebra

Ideal.IsHomogeneous.iff_eq

∀ {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 : Ideal A), Ideal.IsHomogeneous 𝒜 I ↔ (Ideal.homogeneousCore 𝒜 I).toIdeal = I
Defined in
Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal
Cited by
1 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringSetLikeAddSubmonoidClassDecidableEqAddMonoidGradedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ideal.IsHomogeneous.iff_exists · cited by 2IsHomogeneous.iff_existsSemiring · cited by 13802SemiringIdeal · cited by 4748IdealAddMonoid · cited by 2864AddMonoidSetLike · cited by 1084SetLikeGradedRing · cited by 424GradedRingAddSubmonoidClass · cited by 346AddSubmonoidClassHomogeneousIdeal.toIdeal · cited by 105HomogeneousIdeal.toIdealIdeal.IsHomogeneous · cited by 30Ideal.IsHomogeneousIdeal.homogeneousCore · cited by 11Ideal.homogeneousCoreHomogeneousSubmodule.is_homogeneous' · cited by 4HomogeneousSubmodule.is_h…Ideal.IsHomogeneous.toIdeal_homogeneousCore_eq_self · cited by 3IsHomogeneous.toIdeal_hom…IsHomogeneous.iff_eqCITED BYCITES

Cites11

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Cited by1

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