Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.iff_of_isLocalizationAway_of_prime
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [IsNoetherianRing R] {x : R},
Prime x →
∀ (S : Type u_2) [inst_3 : CommRing S] [inst_4 : Algebra R S] [IsLocalization.Away x S],
UniqueFactorizationMonoid R ↔ UniqueFactorizationMonoid S- Defined in
- Mathlib.RingTheory.Ideal.UFD
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 140 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- ENatproof · cited by 4,985
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Disjointproof · cited by 2,201
- IsDomainstatement and proof · cited by 2,196
- Ideal.IsPrimeproof · cited by 827
- Ideal.mapproof · cited by 692
- Submonoid.powersproof · cited by 408
- UniqueFactorizationMonoidstatement and proof · cited by 279
Cited by1
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.iff_localizationAway_of_primeproof · cited by 0