Theorems · Theorem · commutative algebra
LocalizedModule.mk_cancel
∀ {R : Type u} [inst : CommSemiring R] {S : Submonoid R} {M : Type v} [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(s : ↥S) (m : M), LocalizedModule.mk (s • m) s = LocalizedModule.mk m 1- Cited by
- 4 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, 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.
- 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
- one_smulproof · cited by 1,374
- LocalizedModulestatement · cited by 154
- LocalizedModule.mkstatement · cited by 73
- LocalizedModule.mk_eqproof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mkproof · cited by 3
- IsLocalizedModule.mk'_cancelproof · cited by 3
- IsLocalizedModule.mk_eq_mk'proof · cited by 2
- IsLocalizedModule.map_iso_commuteproof · cited by 1