Theorems · Theorem · commutative algebra
Submodule.fg_biSup
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type u_3}
(s : Finset ι) (N : ι → Submodule R M), (∀ i ∈ s, (N i).FG) → (⨆ i ∈ s, N i).FG- Defined in
- Mathlib.RingTheory.Finiteness.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 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.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- iSupstatement · cited by 2,415
- Submodule.FGstatement and proof · cited by 230
- Finset.sup_eq_iSupproof · cited by 30
- Submodule.fg_finset_supproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.fg_iSupproof · cited by 3