Theorems · Definition · commutative algebra
multiplicity_addValuation
{R : Type u_1} → [inst : CommRing R] → [IsDomain R] → {p : R} → Prime p → AddValuation R ℕ∞multiplicity of a prime in an integral domain as an additive valuation to ℕ∞.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 4,985
- IsDomainstatement and proof · cited by 2,196
- Primestatement and proof · cited by 277
- emultiplicityproof · cited by 156
- AddValuationstatement · cited by 96
- AddValuation.ofproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.addValproof · cited by 22
- multiplicity_addValuation_applystatement · cited by 2
- IsDiscreteValuationRing.addVal_le_iff_dvdproof · cited by 1