Theorems · Inductive type · commutative algebra
IsHausdorff
{R : Type u_1} → [inst : CommRing R] → Ideal R → (M : Type u_4) → [inst_1 : AddCommGroup M] → [Module R M] → PropA module M is Hausdorff with respect to an ideal I if ⋂ I^n M = 0.
- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement · cited by 20,661
- CommRingstatement · cited by 17,173
- AddCommGroupstatement · cited by 12,871
- Idealstatement · cited by 4,748
Cited by42
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisorAt.eq_of_mul_add_eq_mul_addstatement and proof · cited by 7
- IsHausdorff.hausstatement and proof · cited by 6
- IsHausdorff.eq_iff_smodEqstatement and proof · cited by 6
- PowerSeries.IsWeierstrassFactorization.elimstatement and proof · cited by 5
- IsHausdorff.haus'statement and proof · cited by 4
- IsHausdorff.subsingletonstatement and proof · cited by 3
- PowerSeries.IsWeierstrassDivision.elimstatement and proof · cited by 3
- Hausdorffification.liftstatement and proof · cited by 3
- AdicCompletion.of_injective_iffstatement and proof · cited by 2
- IsAdic.isHausdorff_iffstatement and proof · cited by 2
- IsHausdorff.of_le_jacobsonstatement · cited by 1
- IsAdicComplete.map_algebraMap_iffproof · cited by 1