Theorems · Theorem · commutative algebra
ModuleCat.hasInjectiveDimensionLE_iff_forall_maximalSpectrum
∀ {R : Type u} [inst : CommRing R] [inst_1 : Small.{v, u} R] [IsNoetherianRing R] (n : ℕ) (M : ModuleCat R),
CategoryTheory.HasInjectiveDimensionLE M n ↔
∀ (m : MaximalSpectrum R), CategoryTheory.HasInjectiveDimensionLE (M.localizedModule m.asIdeal.primeCompl) n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites46
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CommRingstatement and proof · cited by 17,173
- Idealproof · cited by 4,748
- zero_addproof · cited by 2,366
- CategoryTheory.ShortComplexproof · cited by 1,850
- ModuleCatstatement and proof · cited by 1,429
- CategoryTheory.ShortComplex.X₂proof · cited by 1,115
- ModuleCat.carrierproof · cited by 997
- CategoryTheory.Monoproof · cited by 893
- CategoryTheory.ShortComplex.X₃proof · cited by 876
- Ideal.primeComplstatement and proof · cited by 462
- Ideal.IsMaximalproof · cited by 452
Cited by2
Results whose statement or proof uses this declaration.
- ModuleCat.hasInjectiveDimensionLE_iff_forall_primeSpectrumproof · cited by 1
- ModuleCat.injectiveDimension_eq_iSup_localizedModule_maximalproof · cited by 0