Theorems · Theorem · commutative algebra
LocalizedModule.map_id
∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M : Type u_2} [inst_1 : AddCommMonoid M]
[inst_2 : Module R M], (LocalizedModule.map S) LinearMap.id = LinearMap.id- Defined in
- Mathlib.RingTheory.Localization.Module
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Submonoidstatement and proof · cited by 3,086
- LinearMap.extproof · cited by 844
- LinearMap.idstatement · cited by 625
- Localizationstatement · cited by 270
- LocalizedModulestatement and proof · cited by 154
- LinearMap.congr_funproof · cited by 96
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.tilde.map_idproof · cited by 1
- LinearMap.split_surjective_of_localization_maximalproof · cited by 1