Theorems · Theorem · commutative algebra
Submodule.fg_iSup
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Sort u_3}
[Finite ι] (N : ι → Submodule R M), (∀ (i : ι), (N i).FG) → (iSup N).FG- Defined in
- Mathlib.RingTheory.Finiteness.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypeproof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- iSupstatement and proof · cited by 2,415
- nonempty_fintypeproof · cited by 261
- iSup_congr_Propproof · cited by 247
- Submodule.FGstatement and proof · cited by 230
- iSup_posproof · cited by 61
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.Filtration.submodule_fg_iff_stableproof · cited by 1
- Submodule.exists_fg_le_subset_range_rTensor_subtypeproof · cited by 1
- Submodule.exists_fg_le_subset_range_rTensor_inclusionproof · cited by 0