Theorems · Theorem · ring theory
LinearMap.ker_coFG_iff_hasFiniteRange
∀ {K : Type u_1} {V : Type u_2} {V₂ : Type u_4} [inst : Ring K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
[inst_3 : AddCommGroup V₂] [inst_4 : Module K V₂] {f : V →ₗ[K] V₂}, f.ker.CoFG ↔ f.HasFiniteRange- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- LinearMap.kerstatement · cited by 848
- Submodule.CoFGstatement · cited by 28
- LinearMap.HasFiniteRangestatement · cited by 20
- Submodule.range_fg_iff_ker_cofgproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.FiniteRangeSetoid.equiv_iff_eqLocus_coFGproof · cited by 2
- LinearMap.HasFiniteRange.cofg_kerproof · cited by 0