Theorems · Theorem · commutative algebra
IsFractionRing.eq_zero_of_num_eq_zero
∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsDomain A] [inst_2 : UniqueFactorizationMonoid A] {K : Type u_2}
[inst_3 : Field K] [inst_4 : Algebra A K] [inst_5 : IsFractionRing A K] {x : K}, IsFractionRing.num A x = 0 → x = 0- Defined in
- Mathlib.RingTheory.Localization.NumDen
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- IsFractionRingstatement and proof · cited by 738
- UniqueFactorizationMonoidstatement and proof · cited by 279
- IsFractionRing.numstatement and proof · cited by 22
- IsFractionRing.denproof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- IsFractionRing.num_eq_zeroproof · cited by 0