Theorems · Theorem · ring theory
IsSemisimpleModule.congr
∀ {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] [IsSemisimpleModule R M] (e : N ≃ₗ[R] M), IsSemisimpleModule R N- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- LinearEquivstatement and proof · cited by 3,317
- LinearEquiv.symmproof · cited by 1,461
- IsSemisimpleModulestatement and proof · cited by 67
- ComplementedLatticeproof · cited by 30
- Submodule.orderIsoMapComapproof · cited by 16
- OrderIso.complementedLatticeproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- IsSemisimpleModule.of_injectiveproof · cited by 2
- isSemisimpleModule_iff_exists_linearEquiv_dfinsuppproof · cited by 1
- LinearEquiv.isSemisimpleModule_iffproof · cited by 1
- IsSimpleRing.tfaeproof · cited by 1
- IsSemisimpleModule.rangeproof · cited by 0
- IsSemisimpleModule.of_surjectiveproof · cited by 0