Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.coheight_pow_maximalIdeal
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] (n : ℕ), Order.coheight (IsLocalRing.maximalIdeal R ^ n) = ↑n
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- ENatstatement · cited by 4,985
- Idealstatement · cited by 4,748
- IsDomainstatement and proof · cited by 2,196
- OrderDual.toDualproof · cited by 481
- OrderIso.symmproof · cited by 475
- IsLocalRing.maximalIdealstatement · cited by 297
- IsDiscreteValuationRingstatement and proof · cited by 117
- Order.coheightstatement and proof · cited by 74
- IsDiscreteValuationRing.idealOrderIsoENatproof · cited by 5
- Order.coheight_orderIsoproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.length_quotient_pow_maximalIdealproof · cited by 1