Theorems · Definition · commutative algebra
IsDiscreteValuationRing.maximalIdeal
(A : Type u_1) → [inst : CommRing A] → [inst_1 : IsDomain A] → [IsDiscreteValuationRing A] → IsDedekindDomain.HeightOneSpectrum A
The maximal ideal of a discrete valuation ring.
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsDomainstatement and proof · cited by 2,196
- IsDedekindDomain.HeightOneSpectrumstatement · cited by 338
- IsLocalRing.maximalIdealproof · cited by 297
- IsDiscreteValuationRingstatement and proof · cited by 117
Cited by33
Results whose statement or proof uses this declaration.
- WeierstrassCurve.valuation_Δ_auxproof · cited by 5
- WeierstrassCurve.HasGoodReduction.goodReductionstatement · cited by 4
- Ring.ordFrac_eq_valuation_invstatement and proof · cited by 4
- IsDiscreteValuationRing.intValuation_maximalIdealstatement and proof · cited by 3
- WeierstrassCurve.HasAdditiveReduction.additiveReductionstatement · cited by 2
- WeierstrassCurve.HasAdditiveReduction.badReductionstatement · cited by 2
- WeierstrassCurve.HasMultiplicativeReduction.badReductionstatement · cited by 2
- WeierstrassCurve.HasMultiplicativeReduction.multiplicativeReductionstatement · cited by 2
- IsDiscreteValuationRing.exists_lift_of_le_onestatement and proof · cited by 2
- Ring.ordFrac_eq_inverse_comp_valuationstatement and proof · cited by 2
- WeierstrassCurve.hasGoodReduction_iffstatement and proof · cited by 2
- IsDiscreteValuationRing.mker_valuation_eq_isUnitSubmonoidstatement and proof · cited by 2