Theorems · Theorem · ring theory
IsIsotypic.linearEquiv_finsupp
∀ {R : Type u_2} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSemisimpleModule R M]
[Nontrivial M], IsIsotypic R M → ∃ ι, ∃ (_ : Nonempty ι), ∃ S, IsSimpleModule R ↥S ∧ Nonempty (M ≃ₗ[R] ι →₀ ↥S)- Defined in
- Mathlib.RingTheory.SimpleModule.Isotypic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
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
- Submodulestatement and proof · cited by 7,192
- Finsuppstatement and proof · cited by 5,255
- LinearEquivstatement and proof · cited by 3,317
- Nontrivialstatement and proof · cited by 2,416
- IsEmptyproof · cited by 759
- Nonempty.someproof · cited by 340
- isEmpty_or_nonemptyproof · cited by 269
- AddEquiv.toEquivproof · cited by 174
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