Theorems · Theorem · group theory
IsAddTorsion.module_of_finite
∀ (R : Type u_3) (M : Type u_4) [inst : AddCommMonoid M] [inst_1 : Ring R] [Finite R] [Module R M], IsAddTorsion M
A module with a finite ring of scalars is torsion.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddCommMonoidstatement and proof · cited by 12,281
- Ringstatement and proof · cited by 7,463
- Finitestatement and proof · cited by 3,029
- IsAddTorsionstatement · cited by 42
- isAddTorsion_of_finiteproof · cited by 3
- IsAddTorsion.module_of_torsionproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddMonoid.IsTorsion.module_of_finiteproof · cited by 0