Theorems · Theorem · commutative algebra
isAddTorsion_iff_isTorsion_int
∀ {M : Type u_2} [inst : AddCommGroup M], IsAddTorsion M ↔ Module.IsTorsion ℤ M- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- nonZeroDivisorsproof · cited by 895
- ne_of_gtproof · cited by 637
- natCast_zsmulproof · cited by 118
- IsAddTorsionstatement and proof · cited by 42
- mem_nonZeroDivisors_of_ne_zeroproof · cited by 34
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
- Module.IsTorsionstatement and proof · cited by 23
- nonZeroDivisors.coe_ne_zeroproof · cited by 17
- IsOfFinAddOrder.exists_nsmul_eq_zeroproof · cited by 6
- natAbs_nsmul_eq_zeroproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AddCommGroup.finite_of_fg_isAddTorsionproof · cited by 2
- AddMonoid.isTorsion_iff_isTorsion_intproof · cited by 0