Theorems · Theorem · commutative algebra
exact_of_localized_maximal
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} {L : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] [inst_3 : AddCommMonoid N] [inst_4 : Module R N] [inst_5 : AddCommMonoid L]
[inst_6 : Module R L] (f : M →ₗ[R] N) (g : N →ₗ[R] L),
(∀ (J : Ideal R) [inst_7 : J.IsMaximal],
Function.Exact ⇑((LocalizedModule.map J.primeCompl) f) ⇑((LocalizedModule.map J.primeCompl) g)) →
Function.Exact ⇑f ⇑g- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 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 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
- Function.Exactstatement and proof · cited by 182
- LocalizedModulestatement and proof · cited by 154
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.