Theorems · Theorem · commutative algebra
AdicCompletion.map_id
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (M : Type u_2) [inst_1 : AddCommGroup M] [inst_2 : Module R M],
AdicCompletion.map I LinearMap.id = LinearMap.id- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- Idealstatement and proof · cited by 4,748
- LinearMap.idstatement and proof · cited by 625
- Submodule.Quotient.mkproof · cited by 184
- AdicCompletionstatement · cited by 160
- AdicCompletion.AdicCauchySequenceproof · cited by 41
- AdicCompletion.mapstatement · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- AdicCompletion.pow_smul_top_eq_ker_evalproof · cited by 4
- AdicCompletion.piEquivOfFintype_applyproof · cited by 1