Theorems · Definition · commutative algebra
IsLocalization.finsetIntegerMultiple
{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] → [DecidableEq R] → Finset S → Finset RThe finset of numerators after clearing the denominators of a finite set of fractions.
- Defined in
- Mathlib.RingTheory.Localization.Integer
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Finset.imageproof · cited by 910
- IsLocalizationstatement and proof · cited by 636
- Finset.attachproof · cited by 168
- IsLocalization.integerMultipleproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- IsLocalization.finsetIntegerMultiple_imagestatement · cited by 3
- Algebra.FiniteType.of_span_eq_top_targetproof · cited by 2
- IsLocalization.exists_smul_mem_of_mem_adjoinstatement and proof · cited by 2
- IsLocalization.finsetIntegerMultiple.congr_simpstatement and proof · cited by 2
- IsLocalization.card_finsetIntegerMultiplestatement · cited by 1
- IsFractionRing.finrank_left_eqproof · cited by 1
- IsLocalization.lift_mem_adjoin_finsetIntegerMultiplestatement and proof · cited by 1
- IsLocalization.linearIndepOn_finsetIntegerMultiplestatement · cited by 1
- IsLocalization.smul_mem_finsetIntegerMultiple_spanstatement and proof · cited by 1
- Algebra.FiniteType.of_span_eq_top_sourceproof · cited by 1
- RingHom.finite_ofLocalizationSpanproof · cited by 0