Theorems · Theorem · commutative algebra

IsFractionRing.num_den_unique

∀ (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) (n : A) (d : ↥(nonZeroDivisors A)),
  IsRelPrime n ↑d →
    IsLocalization.mk' K n d = x → Associated (IsFractionRing.num A x) n ∧ Associated ↑(IsFractionRing.den A x) ↑d

Defined in

Mathlib.RingTheory.Localization.NumDen

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainUniqueFactorizationMonoidFieldAlgebraIsFractionRing