Theorems · Theorem · ring theory
IsSemisimpleModule.sup
∀ {R : Type u_2} [inst : Ring R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {p q : Submodule R M},
IsSemisimpleModule R ↥p → IsSemisimpleModule R ↥q → IsSemisimpleModule R ↥(p ⊔ q)- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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Cites10
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
- Set.univproof · cited by 3,945
- iSupproof · cited by 2,415
- IsSemisimpleModulestatement and proof · cited by 67
- iSup_bool_eqproof · cited by 12
- iSup_univproof · cited by 8
- isSemisimpleModule_biSup_of_isSemisimpleModule_submoduleproof · cited by 2
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