Theorems · Theorem · commutative algebra
ModuleCat.projectiveDimension_quotient_eq_length
∀ {R : Type u} [inst : CommRing R] [inst_1 : Small.{v, u} R] [IsLocalRing R] [IsNoetherianRing R] (rs : List R),
RingTheory.Sequence.IsRegular R rs →
CategoryTheory.projectiveDimension (ModuleCat.of R (Shrink.{v, u} (R ⧸ Ideal.ofList rs))) = ↑rs.length- Cited by
- 0 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- HasQuotient.Quotientstatement and proof · cited by 2,301
- WithBotstatement and proof · cited by 1,498
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