Theorems · Theorem · group theory
IsAddTorsion.module_of_torsion
∀ (R : Type u_3) (M : Type u_4) [inst : AddCommMonoid M] [inst_1 : Semiring R] [Module R M], IsAddTorsion R → IsAddTorsion M
A module whose scalars are torsion is torsion.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoidSemiringModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- zero_smulproof · cited by 716
- Nat.cast_smul_eq_nsmulproof · cited by 110
- IsAddTorsionstatement and proof · cited by 42
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
- IsOfFinAddOrder.exists_nsmul_eq_zeroproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- IsAddTorsion.module_of_finiteproof · cited by 1
- AddMonoid.IsTorsion.module_of_torsionproof · cited by 0