Theorems · Theorem · commutative algebra
injective_of_localized_maximal
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : AddCommMonoid N] [inst_4 : Module R N] (f : M →ₗ[R] N),
(∀ (J : Ideal R) [inst_5 : J.IsMaximal], Function.Injective ⇑((LocalizedModule.map J.primeCompl) f)) →
Function.Injective ⇑f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- Idealstatement and proof · cited by 4,748
- Ideal.primeComplstatement and proof · cited by 462
- Ideal.IsMaximalstatement and proof · cited by 452
- Localizationstatement · cited by 270
- LocalizedModulestatement and proof · cited by 154
- LocalizedModule.mkLinearMapproof · cited by 76
Cited by1
Results whose statement or proof uses this declaration.
- bijective_of_localized_maximalproof · cited by 1