Theorems · Definition · commutative algebra
AdicCompletion.AdicCauchySequence
{R : Type u_1} → [inst : CommRing R] → Ideal R → (M : Type u_4) → [inst_1 : AddCommGroup M] → [Module R M] → Type u_4The type of I-adic Cauchy sequences.
- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 72 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Idealstatement and proof · cited by 4,748
- AdicCompletion.IsAdicCauchyproof · cited by 19
Cited by46
Results whose statement or proof uses this declaration.
- AdicCompletion.mkstatement and proof · cited by 22
- AdicCompletion.AdicCauchySequence.mapstatement and proof · cited by 11
- AdicCompletion.mk_apply_coestatement and proof · cited by 10
- AdicCompletion.induction_onstatement and proof · cited by 9
- AdicCompletion.map_ext'statement and proof · cited by 6
- AdicCompletion.AdicCauchySequence.map_apply_coestatement and proof · cited by 5
- AdicCompletion.AdicCauchySequence.mkstatement · cited by 4
- AdicCompletion.AdicCauchySequence.mk_eq_mkstatement and proof · cited by 3
- AdicCompletion.map_compproof · cited by 3
- AdicCompletion.map_idproof · cited by 2
- AdicCompletion.map_surjectiveproof · cited by 2
- AdicCompletion.mkₐstatement · cited by 2