Theorems · Theorem · ring theory
IsSemisimpleModule.exists_linearEquiv_dfinsupp
∀ (R : Type u_2) [inst : Ring R] (M : Type u_4) [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSemisimpleModule R M], ∃ s x, sSupIndep s ∧ ∀ (m : ↑s), IsSimpleModule R ↥↑m
- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Set.Elemstatement and proof · cited by 7,166
- LinearEquivstatement and proof · cited by 3,317
- iSupproof · cited by 2,415
- LinearEquiv.symmproof · cited by 1,461
Cited by3
Results whose statement or proof uses this declaration.
- IsIsotypicOfType.linearEquiv_finsuppproof · cited by 1
- isSemisimpleModule_iff_exists_linearEquiv_dfinsuppproof · cited by 1
- IsSemisimpleModule.exists_linearEquiv_fin_dfinsuppproof · cited by 1