Theorems · Theorem · commutative algebra
Submodule.CoFG.fg_of_isCompl
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {S T : Submodule R M},
IsCompl S T → S.CoFG → T.FGA complement of a CoFG submodule is FG.
- Defined in
- Mathlib.RingTheory.Finiteness.Cofinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- IsComplstatement and proof · cited by 351
- Submodule.FGstatement · cited by 230
- Submodule.CoFGstatement and proof · cited by 28
- Submodule.quotientEquivOfIsComplproof · cited by 23
- Module.Finite.iff_fgproof · cited by 21
- Module.Finite.equivproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.isClosed_range_of_isClosed_map_of_finiteDimensional_quotientproof · cited by 0