Theorems · Theorem · commutative algebra
IsLocalization.integerMultiple_injective
∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) {S : Type u_2} [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [inst_3 : IsLocalization M S] {ι : Type u_4} (s : Finset ι) (f : ι → S),
Function.Injective f → Function.Injective (IsLocalization.integerMultiple M s f)- Defined in
- Mathlib.RingTheory.Localization.Integer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 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
- Finsetstatement and proof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- Function.Bijective.injectiveproof · cited by 115
- SetLike.coe_eq_coeproof · cited by 21
- IsLocalization.integerMultiplestatement and proof · cited by 5
- IsLocalization.commonDenomproof · cited by 4
- IsLocalization.map_integerMultipleproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.card_finsetIntegerMultipleproof · cited by 1
- IsLocalization.integerMultipleMultiple_injectiveproof · cited by 0