Theorems · Theorem · commutative algebra
IsLocalizedModule.Away.surj
∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_2} {N : Type u_3} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] (f : M →ₗ[R] N) (r : R)
[IsLocalizedModule.Away r f] (y : N), ∃ n x, r ^ n • y = f x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Submonoid.powersproof · cited by 408
- IsLocalizedModule.Awaystatement and proof · cited by 27
- IsLocalizedModule.surjproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalizedModule.Away.of_associatedproof · cited by 1