Theorems · Definition · commutative algebra
ValuativeRel.valuation
(R : Type u_2) → [inst : Ring R] → [inst_1 : ValuativeRel R] → Valuation R (ValuativeRel.ValueGroupWithZero R)
The "canonical" valuation associated to a valuative relation.
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingValuativeRel
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.
- Ringstatement and proof · cited by 7,463
- Valuationstatement · cited by 823
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.ValueGroupWithZerostatement · cited by 86
- ValuativeRel.ValueGroupWithZero.mkproof · cited by 25
Cited by48
Results whose statement or proof uses this declaration.
- Valuation.mem_nhds_iffproof · cited by 6
- ValuativeExtension.mapValueGroupWithZeroproof · cited by 5
- ValuativeRel.ValueGroupWithZero.embed_strictMonoproof · cited by 4
- ValuativeRel.valuation_eq_zero_iffstatement · cited by 3
- ValuativeRel.ValueGroupWithZero.mk_eq_divstatement · cited by 3
- ValuativeRel.ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀statement · cited by 3
- ValuativeRel.exists_valuation_div_valuation_eqstatement · cited by 2
- ValuativeRel.ValueGroupWithZero.embed_valuation_eq_restrict₀statement and proof · cited by 2
- Valuation.exists_setOfPred_restrict_le_iffstatement and proof · cited by 2
- IsValuativeTopology.hasBasis_nhdsstatement and proof · cited by 2
- IsValuativeTopology.hasBasis_nhds_zerostatement and proof · cited by 2
- IsValuativeTopology.mem_nhds_iffstatement · cited by 2