Theorems · Theorem · linear algebra
finrank_quotient_torsion_eq
∀ {M : Type u_1} [inst : AddCommGroup M],
Module.finrank ℤ (M ⧸ AddSubgroup.toIntSubmodule (AddCommGroup.torsion M)) = Module.finrank ℤ MQuotienting an additive commutative group by its torsion subgroup does not change its
ℤ-finrank.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement and proof · cited by 7,192
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- Module.finrankstatement · cited by 1,770
- OrderIsostatement · cited by 874
- le_of_eqproof · cited by 366
- AddSubgroup.toIntSubmodulestatement and proof · cited by 25
- AddCommGroup.torsionstatement · cited by 18
- Submodule.torsionproof · cited by 15
- finrank_quotient_eq_of_le_torsionproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.Units.finrank_eqproof · cited by 0