Theorems · Theorem · group theory
Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModule
∀ {k : Type u_1} {G : Type u_2} [inst : Monoid G] [inst_1 : Field k] (M : Type u_4) [inst_2 : AddCommGroup M]
[inst_3 : Module (MonoidAlgebra k G) M],
IsSemisimpleModule (MonoidAlgebra k G) M ↔ (Representation.ofModule M).IsSemisimpleRepresentation- Defined in
- Mathlib.RepresentationTheory.Semisimple
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Fieldstatement and proof · cited by 7,404
- Monoidstatement and proof · cited by 3,887
- MonoidAlgebrastatement and proof · cited by 590
- IsSemisimpleModulestatement · cited by 67
- RestrictScalarsstatement · cited by 18
- Representation.ofModulestatement and proof · cited by 11
- OrderIso.complementedLattice_iffproof · cited by 8
- isSemisimpleModule_iffproof · cited by 5
- Subrepresentation.submoduleSubrepresentationOrderIsoproof · cited by 4
- Representation.IsSemisimpleRepresentationstatement and proof · cited by 2
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