Theorems · Theorem · commutative algebra
Submodule.CoFG.ker
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_3}
[inst_3 : AddCommGroup N] [inst_4 : Module R N] [IsNoetherian R N] (f : M →ₗ[R] N), f.ker.CoFGThe kernel of a linear map into a noetherian module is CoFG.
- Defined in
- Mathlib.RingTheory.Finiteness.Cofinite
- Cited by
- 1 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.
Cites11
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.rangeproof · cited by 893
- LinearMap.kerstatement · cited by 848
- IsNoetherianstatement and proof · cited by 208
- IsNoetherian.noetherianproof · cited by 32
- Submodule.CoFGstatement · cited by 28
- Submodule.range_fg_iff_ker_cofgproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.CoFG.infproof · cited by 1