Theorems · Definition · commutative algebra
ValuationSubring.valuation
{K : Type u} → [inst : Field K] → (A : ValuationSubring K) → Valuation K A.ValueGroupAny valuation subring of K induces a natural valuation on K.
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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.
- Fieldstatement and proof · cited by 7,404
- Valuationstatement · cited by 823
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.ValueGroupstatement · cited by 26
- ValuationRing.valuationproof · cited by 5
Cited by32
Results whose statement or proof uses this declaration.
- ValuationSubring.unitGroupproof · cited by 16
- ValuationSubring.nonunitsproof · cited by 14
- ValuationSubring.principalUnitGroupproof · cited by 11
- ValuationSubring.valuation_le_one_iffstatement · cited by 9
- ValuationSubring.valuation_lt_one_iffstatement and proof · cited by 4
- ValuationSubring.valuation_le_onestatement · cited by 3
- ValuationSubring.mem_nonunits_iffstatement · cited by 2
- ValuationSubring.ofPrime_idealOfLEproof · cited by 2
- Valuation.isEquiv_valuation_valuationSubringstatement · cited by 2
- ValuationSubring.valuation_eq_one_iffstatement and proof · cited by 2
- ValuationSubring.mapOfLE_valuation_applystatement · cited by 1
- ValuationSubring.mem_nonunits_iff_orproof · cited by 1