Theorems · Theorem · commutative algebra
Submodule.CoFG.inf
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsNoetherianRing R]
{S T : Submodule R M}, S.CoFG → T.CoFG → (S ⊓ T).CoFGOver a noetherian ring the intersection of two CoFG submodules is CoFG.
- Defined in
- Mathlib.RingTheory.Finiteness.Cofinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- LinearMap.kerproof · cited by 848
- IsNoetherianRingstatement and proof · cited by 268
- Submodule.mkQproof · cited by 232
- Submodule.ker_mkQproof · cited by 63
- LinearMap.prodproof · cited by 32
- Submodule.CoFGstatement and proof · cited by 28
- LinearMap.ker_prodproof · cited by 4
- Submodule.CoFG.kerproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.CoFG.sInfproof · cited by 1