Theorems · Definition · commutative algebra
LocalizedModule
{R : Type u} →
[inst : CommSemiring R] → Submonoid R → (M : Type v) → [inst_1 : AddCommMonoid M] → [Module R M] → Type (max u v)If S is a multiplicative subset of a ring R and M an R-module, then
we can localize M by S.
- Cited by
- 154 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 207 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- OreLocalizationproof · cited by 90
Cited by188
Results whose statement or proof uses this declaration.
- LocalizedModule.mkLinearMapstatement · cited by 76
- LocalizedModule.mkstatement · cited by 73
- Module.supportproof · cited by 52
- Module.rankAtStalkproof · cited by 41
- IsLocalizedModule.isostatement and proof · cited by 34
- DivisibleHullproof · cited by 30
- LocalizedModule.mapstatement · cited by 29
- LocalizedModule.Awayproof · cited by 20
- ModuleCat.localizedModuleproof · cited by 16
- LocalizedModule.mkLinearMap_applystatement · cited by 16
- AlgebraicGeometry.StructureSheaf.Localizationsproof · cited by 15
- Module.freeLocusproof · cited by 15