Theorems · Theorem · commutative algebra
AdicCompletion.map_surjective
∀ {R : Type u} [inst : CommRing R] (I : Ideal R) {M : Type v} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{N : Type w} [inst_3 : AddCommGroup N] [inst_4 : Module R N] {f : M →ₗ[R] N},
Function.Surjective ⇑f → Function.Surjective ⇑(AdicCompletion.map I f)Adic completion preserves surjectivity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Top.topproof · cited by 9,680
- Set.Elemproof · cited by 7,166
- Set.preimageproof · cited by 4,946
- Idealstatement and proof · cited by 4,748
- Submodule.Quotient.mkproof · cited by 184
- AdicCompletionstatement and proof · cited by 160
Cited by2
Results whose statement or proof uses this declaration.
- AdicCompletion.pow_smul_top_eq_ker_evalproof · cited by 4
- AdicCompletion.ofTensorProduct_surjective_of_finiteproof · cited by 0