Theorems · Definition · commutative algebra
ValuationSubring.subtype
{K : Type u} → [inst : Field K] → (R : ValuationSubring K) → ↥R →+* KThe canonical ring homomorphism from a valuation ring to its field of fractions.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 53 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.
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.toSubringproof · cited by 32
- Subring.subtypeproof · cited by 22
Cited by4
Results whose statement or proof uses this declaration.
- ValuationSubring.unitGroupMulEquivproof · cited by 7
- ValuationSubring.subtype_injectivestatement · cited by 0
- ValuationSubring.subtype_applystatement · cited by 0
- ValuationSubring.coe_subtypestatement · cited by 0