Theorems · Theorem · ring theory
isSemisimpleModule_biSup_of_isSemisimpleModule_submodule
∀ {ι : Type u_1} {R : Type u_2} [inst : Ring R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{s : Set ι} {p : ι → Submodule R M}, (∀ i ∈ s, IsSemisimpleModule R ↥(p i)) → IsSemisimpleModule R ↥(⨆ i ∈ s, p i)- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- 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
- iSupstatement and proof · cited by 2,415
- Submodule.range_subtypeproof · cited by 82
- IsSemisimpleModulestatement and proof · cited by 67
- Submodule.injective_subtypeproof · cited by 43
- le_biSupproof · cited by 20
- Submodule.biSup_comap_subtype_eq_topproof · cited by 5
- isSemisimpleModule_of_isSemisimpleModule_submoduleproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.le_linearEquiv_of_le_sSupproof · cited by 2
- IsSemisimpleModule.supproof · cited by 0