Theorems · Definition · commutative algebra
ValuationSubring.ValueGroup
{K : Type u} → [inst : Field K] → ValuationSubring K → Type uThe value group of the valuation associated to A. Note: it is actually a group with zero.
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 67 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.
Cites3
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
- ValuationSubringstatement and proof · cited by 187
- ValuationRing.ValueGroupproof · cited by 6
Cited by28
Results whose statement or proof uses this declaration.
- ValuationSubring.valuationstatement · cited by 29
- ValuationSubring.valuation_le_one_iffstatement · cited by 9
- ValuationSubring.mapOfLEstatement · cited by 6
- ValuationSubring.valuation_lt_one_iffstatement · cited by 4
- ValuationSubring.monotone_mapOfLEstatement and proof · cited by 3
- ValuationSubring.valuation_le_onestatement · cited by 3
- ValuationSubring.mem_nonunits_iffstatement · cited by 2
- Valuation.isEquiv_valuation_valuationSubringstatement · cited by 2
- ValuationSubring.valuation_eq_one_iffstatement and proof · cited by 2
- ValuationSubring.ofPrime_idealOfLEproof · cited by 2
- ValuationSubring.mapOfLE_valuation_applystatement · cited by 1
- ValuationSubring.mem_of_valuation_le_onestatement · cited by 1