Theorems · Definition · commutative algebra
LocalizedModule.mk
{R : Type u} →
[inst : CommSemiring R] →
{S : Submonoid R} → {M : Type v} → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → M → ↥S → LocalizedModule S MThe canonical map sending (m, s) ↦ m/s
- Cited by
- 73 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- LocalizedModulestatement · cited by 154
- OreLocalization.oreDivproof · cited by 72
Cited by82
Results whose statement or proof uses this declaration.
- LocalizedModule.mkLinearMapproof · cited by 76
- IsLocalizedModule.mk'proof · cited by 54
- AlgebraicGeometry.StructureSheaf.constproof · cited by 20
- DivisibleHull.mkproof · cited by 19
- LocalizedModule.mkLinearMap_applystatement · cited by 16
- LocalizedModule.mk_eqstatement and proof · cited by 15
- LocalizedModule.smul'_mkstatement and proof · cited by 13
- LocalizedModule.induction_onstatement and proof · cited by 11
- IsLocalizedModule.mk'_smulproof · cited by 6
- IsLocalizedModule.iso_mk_onestatement · cited by 5
- IsLocalizedModule.iso_symm_compproof · cited by 5
- LocalizedModule.induction_on₂statement and proof · cited by 5