Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.of_isLocalization
∀ {M : Type u_1} [inst : CommSemiring M] (S : Submonoid M) (N : Type u_3) [inst_1 : CommSemiring N]
[inst_2 : Algebra M N] [IsLocalization S N] [UniqueFactorizationMonoid M], UniqueFactorizationMonoid NA localization of a unique factorization monoid is still a unique factorization monoid.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- UniqueFactorizationMonoidstatement and proof · cited by 279
- IsLocalization.toLocalizationMapproof · cited by 69
- Submonoid.LocalizationMap.uniqueFactorizationMonoidproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.iff_of_isLocalizationAway_of_primeproof · cited by 1