Theorems · Theorem · ring theory
LinearEquiv.isSemisimpleModule_iff
∀ {R : Type u_2} [inst : Ring R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_5}
[inst_3 : AddCommGroup N] [inst_4 : Module R N] (e : M ≃ₗ[R] N), IsSemisimpleModule R M ↔ IsSemisimpleModule R N- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- LinearEquivstatement and proof · cited by 3,317
- LinearEquiv.symmproof · cited by 1,461
- IsSemisimpleModulestatement and proof · cited by 67
- IsSemisimpleModule.congrproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- isSemisimpleModule_biSup_of_isSemisimpleModule_submoduleproof · cited by 2