Theorems · Theorem · commutative algebra
IsLocalization.map_integerMultiple
∀ {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) (i : ↥s),
(algebraMap R S) (IsLocalization.integerMultiple M s f i) = IsLocalization.commonDenom M s f • f ↑i- Defined in
- Mathlib.RingTheory.Localization.Integer
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- Subtype.propproof · cited by 505
- IsLocalization.integerMultiplestatement · cited by 5
- IsLocalization.exist_integer_multiplesproof · cited by 4
- IsLocalization.commonDenomstatement · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- IsLocalization.finsetIntegerMultiple_imageproof · cited by 3
- IsLocalization.integerMultiple_injectiveproof · cited by 2
- IsLocalization.scaleRoots_commonDenom_mem_liftsproof · cited by 1