Theorems · Inductive type · commutative algebra
Valuation
(R : Type u_3) → (Γ₀ : Type u_4) → [LinearOrderedCommMonoidWithZero Γ₀] → [Ring R] → Type (max u_3 u_4)
The type of Γ₀-valued valuations on R.
When you extend this structure, make sure to extend ValuationClass.
- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 823 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 3 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement · cited by 7,463
- LinearOrderedCommMonoidWithZerostatement · cited by 139
Cited by975
Results whose statement or proof uses this declaration.
- Valued.vstatement · cited by 163
- WithValstatement · cited by 151
- IsDedekindDomain.HeightOneSpectrum.valuationstatement · cited by 130
- Valuation.restrictstatement and proof · cited by 112
- AddValuationproof · cited by 96
- Valuation.Compatiblestatement · cited by 71
- Valuation.integerstatement and proof · cited by 68
- Valuation.IsEquivstatement and proof · cited by 67
- Valuation.Integersstatement · cited by 58
- Valuation.valuationSubringstatement and proof · cited by 56
- IsDedekindDomain.HeightOneSpectrum.intValuationstatement · cited by 53
- Valuation.IsRankOneDiscretestatement · cited by 53
Showing the 200 most cited of 975.