Theorems · Theorem · ring theory
IsSemisimpleModule.exists_simple_submodule
∀ (R : Type u_2) [inst : Ring R] (M : Type u_4) [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSemisimpleModule R M] [Nontrivial M], ∃ m, IsSimpleModule R ↥m
- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites8
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
- Nontrivialstatement and proof · cited by 2,416
- IsSimpleModulestatement · cited by 114
- IsSemisimpleModulestatement and proof · cited by 67
- IsAtomic.exists_atomproof · cited by 4
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