Theorems · Theorem · commutative algebra
ModuleCat.injectiveDimension_eq_iSup_localizedModule_prime
∀ {R : Type u} [inst : CommRing R] [inst_1 : Small.{v, u} R] [IsNoetherianRing R] (M : ModuleCat R),
CategoryTheory.injectiveDimension M = ⨆ p, CategoryTheory.injectiveDimension (M.localizedModule p.asIdeal.primeCompl)- Cited by
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- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- ENatstatement and proof · cited by 4,985
- Idealproof · cited by 4,748
- iSupstatement and proof · cited by 2,415
- WithBotstatement and proof · cited by 1,498
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierproof · cited by 997
- PrimeSpectrumstatement and proof · cited by 625
- ModuleCat.ofproof · cited by 594
- Ideal.primeComplstatement and proof · cited by 462
- Ideal.IsMaximalproof · cited by 452
- Smallstatement and proof · cited by 369
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