Theorems · Theorem · commutative algebra
Ring.ordFrac_eq_ord
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsNoetherianRing R] [inst_2 : Ring.KrullDimLE 1 R] {K : Type u_3}
[inst_3 : Field K] [inst_4 : Algebra R K] [inst_5 : IsFractionRing R K] [inst_6 : Nontrivial R] {x : R},
x ≠ 0 → (Ring.ordFrac R) ((algebraMap R K) x) = (Ring.ordMonoidWithZeroHom R) x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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 and proof · cited by 4,706
- Nontrivialstatement and proof · cited by 2,416
- IsDomainproof · cited by 2,196
- nonZeroDivisorsproof · cited by 895
- Multiplicativestatement · cited by 875
- IsFractionRingstatement and proof · cited by 738
- MonoidWithZeroHomstatement · cited by 704
Cited by4
Results whose statement or proof uses this declaration.
- Ring.ordFrac_of_isUnitproof · cited by 1
- Ring.ordFrac_ge_one_of_ne_zeroproof · cited by 1
- Ring.ordFrac_eq_intValuationproof · cited by 1
- Ring.ordFrac_eq_divproof · cited by 0