Theorems · Definition · commutative algebra
AddSubgroup.torsionBy
(A : Type u_3) → [inst : AddCommGroup A] → ℤ → AddSubgroup A
The additive n-torsion subgroup for an integer n, denoted as A[n].
- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommGroup
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.
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroupstatement · cited by 3,232
- Submodule.toAddSubgroupproof · cited by 106
- Submodule.torsionByproof · cited by 31
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.torsionBy.nsmulstatement and proof · cited by 1
- AddSubgroup.torsionBy.nsmul_iffstatement · cited by 1
- AddSubgroup.torsionBy.mod_self_nsmulstatement and proof · cited by 0
- AddSubgroup.torsionBy.mod_self_nsmul'statement and proof · cited by 0
- AddSubgroup.torsionBy.negstatement · cited by 0
- AddSubgroup.torsionBy.zmodModulestatement · cited by 0