Theorems · Theorem · ring theory
IsSemisimpleRing.exists_linearEquiv_ideal_of_isSimpleModule
∀ (R : Type u_2) [inst : Ring R] (M : Type u_4) [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSemisimpleRing R] [h : IsSimpleModule R M], ∃ I, Nonempty (M ≃ₗ[R] ↥I)
- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- LinearEquivstatement and proof · cited by 3,317
- HasQuotient.Quotientproof · cited by 2,301
- LinearEquiv.symmproof · cited by 1,461
- Ideal.IsMaximalproof · cited by 452
- LinearEquiv.transproof · cited by 298
- IsSimpleModulestatement and proof · cited by 114
Cited by1
Results whose statement or proof uses this declaration.
- IsIsotypic.of_selfproof · cited by 1