Theorems · Theorem · commutative algebra
IsLocalization.exist_integer_multiples_of_finset
∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) {S : Type u_2} [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [IsLocalization M S] (s : Finset S), ∃ b, ∀ a ∈ s, IsLocalization.IsInteger R (↑b • a)We can clear the denominators of a finite set of fractions.
- Defined in
- Mathlib.RingTheory.Localization.Integer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 58 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.
- Finsetstatement and proof · cited by 13,712
- 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
- IsLocalization.IsIntegerstatement · cited by 39
- IsLocalization.exist_integer_multiplesproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.isFractional_of_fgproof · cited by 2