Theorems · Theorem · commutative algebra

HomogeneousIdeal.toIdeal_iInf

∀ {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] {κ : Sort u_4}
  (s : κ → HomogeneousIdeal 𝒜), (⨅ i, s i).toIdeal = ⨅ i, (s i).toIdeal

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal

Cited by

3 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringDecidableEqAddMonoidSetLikeAddSubmonoidClassGradedRing