Theorems · Theorem · commutative algebra
Submodule.fg_iff_exists_fin_linearMap
∀ (R : Type u_1) (M : Type u_2) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{N : Submodule R M}, N.FG ↔ ∃ n f, f.range = N- Cited by
- 4 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Set.rangeproof · cited by 4,705
- Finiteproof · cited by 3,029
- SMulCommClassproof · cited by 1,927
- Submodule.spanproof · cited by 1,504
- LinearMap.rangestatement and proof · cited by 893
- Submodule.FGstatement · cited by 230
Cited by4
Results whose statement or proof uses this declaration.
- Module.Finite.exists_fin'proof · cited by 10
- AddSubmonoid.fg_iff_exists_fin_addMonoidHomproof · cited by 4
- Module.FinitePresentation.exists_fin'proof · cited by 1
- AddSubgroup.fg_iff_exists_fin_addMonoidHomproof · cited by 0