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Theorems · Theorem · commutative algebra

Ideal.homogeneousCore.gc

∀ {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],
  GaloisConnection HomogeneousIdeal.toIdeal (Ideal.homogeneousCore 𝒜)
Defined in
Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal
Cited by
2 results in Mathlib
Foundations
Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringDecidableEqAddMonoidSetLikeAddSubmonoidClassGradedRing
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Around this declaration

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

Ideal.homogeneousCore'_eq_sSup · cited by 0Ideal.homogeneousCore'_eq…Ideal.homogeneousCore.gi · cited by 0homogeneousCore.giIdeal.homogeneousCore_eq_sSup · cited by 0Ideal.homogeneousCore_eq_…Semiring · cited by 13802SemiringIdeal · cited by 4748IdealAddMonoid · cited by 2864AddMonoidSetLike · cited by 1084SetLikele_trans · cited by 985le_transGradedRing · cited by 424GradedRingAddSubmonoidClass · cited by 346AddSubmonoidClassGaloisConnection · cited by 253GaloisConnectionHomogeneousIdeal · cited by 115HomogeneousIdealHomogeneousIdeal.toIdeal · cited by 105HomogeneousIdeal.toIdealIdeal.homogeneousCore · cited by 11Ideal.homogeneousCoreIdeal.homogeneousCore'_le · cited by 3Ideal.homogeneousCore'_leIdeal.homogeneousCore_mono · cited by 2Ideal.homogeneousCore_monoHomogeneousIdeal.toIdeal_homogeneousCore_eq_self · cited by 1HomogeneousIdeal.toIdeal_…homogeneousCore.gcCITED BYCITES

Cites14

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Cited by3

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