Theorems · Theorem · commutative algebra
Ring.ordFrac_eq_intValuation
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {K : Type u_2}
[inst_3 : Field K] [inst_4 : Algebra R K] [inst_5 : IsFractionRing R K] {x : R},
x ≠ 0 → (Ring.ordFrac R) ((algebraMap R K) x) = ((IsDiscreteValuationRing.maximalIdeal R).intValuation x)⁻¹- Cited by
- 1 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- Multiplicativestatement and proof · cited by 875
- Valuationstatement · cited by 823
- IsFractionRingstatement and proof · cited by 738
- MonoidWithZeroHomstatement · cited by 704
- WithZerostatement and proof · cited by 586
Cited by1
Results whose statement or proof uses this declaration.
- Ring.ordFrac_eq_inverse_comp_valuationproof · cited by 2