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Theorems · Theorem · commutative algebra

Ideal.homogeneousHull_mono

∀ {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],
  Monotone (Ideal.homogeneousHull 𝒜)
Defined in
Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal
Cited by
1 results in Mathlib
Foundations
Depth 104 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.homogeneousHull.gc · cited by 1homogeneousHull.gcDFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringSet.ofPred · cited by 6101Set.ofPredIdeal · cited by 4748IdealAddMonoid · cited by 2864AddMonoidMonotone · cited by 1397MonotoneSetLike · cited by 1084SetLikeGradedRing · cited by 424GradedRingAddSubmonoidClass · cited by 346AddSubmonoidClassHomogeneousIdeal · cited by 115HomogeneousIdealDirectSum.decompose · cited by 93DirectSum.decomposeIdeal.span_mono · cited by 16Ideal.span_monoIdeal.homogeneousHull · cited by 8Ideal.homogeneousHullIdeal.homogeneousHull_monoCITED BYCITES

Cites13

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Cited by1

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