Theorems · Theorem · commutative algebra
Submodule.FG.cofg_of_codisjoint
∀ {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},
Codisjoint S T → S.FG → T.CoFGIf S and T are co-disjoint and S is FG, then T is CoFG.
- 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.
Cites16
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
- Top.topproof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Module.Finiteproof · cited by 1,032
- Submodule.mkQproof · cited by 232
- Submodule.FGstatement and proof · cited by 230
- Codisjointstatement and proof · cited by 197
- LinearMap.domRestrictproof · cited by 45
- Module.Finite.of_surjectiveproof · cited by 29
- Submodule.CoFGstatement · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.FG.cofg_of_isComplproof · cited by 0