Theorems · Theorem · commutative algebra
AdicCompletion.of_surjective_iff
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M],
Function.Surjective ⇑(AdicCompletion.of I M) ↔ IsPrecomplete I M- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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 · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientproof · cited by 2,301
- Submodule.Quotient.mkproof · cited by 184
- AdicCompletionstatement and proof · cited by 160
- SModEqproof · cited by 80
Cited by2
Results whose statement or proof uses this declaration.
- AdicCompletion.of_surjectiveproof · cited by 1
- AdicCompletion.of_bijective_iffproof · cited by 1