Theorems · Theorem · commutative algebra
Submodule.CoFG.sInf
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsNoetherianRing R]
{s : Finset (Submodule R M)}, (∀ S ∈ s, S.CoFG) → (sInf ↑s).CoFGOver a noetherian ring the infimum of a finite family of CoFG submodules is CoFG.
- Defined in
- Mathlib.RingTheory.Finiteness.Cofinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- InfSet.sInfstatement and proof · cited by 935
- IsNoetherianRingstatement and proof · cited by 268
- Finset.coe_insertproof · cited by 124
- Finset.coe_emptyproof · cited by 109
- Finset.inductionproof · cited by 108
- Submodule.CoFGstatement and proof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.CoFG.sInf_of_finiteproof · cited by 0