Theorems · Theorem · commutative algebra

Ideal.IsHomogeneous.radical_eq

∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : CommRing A] [inst_1 : AddCommMonoid ι] [inst_2 : LinearOrder ι]
  [IsOrderedCancelAddMonoid ι] [inst_4 : SetLike σ A] [inst_5 : AddSubmonoidClass σ A] {𝒜 : ι → σ}
  [inst_6 : GradedRing 𝒜] {I : Ideal A},
  Ideal.IsHomogeneous 𝒜 I → I.radical = sInf {J | Ideal.IsHomogeneous 𝒜 J ∧ I ≤ J ∧ J.IsPrime}

Defined in

Mathlib.RingTheory.GradedAlgebra.Radical

Cited by

1 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommMonoidLinearOrderIsOrderedCancelAddMonoidSetLikeAddSubmonoidClassGradedRing