Theorems · Theorem · ring theory

IsIsotypicOfType.linearEquiv_finsupp

∀ {R : Type u_2} {M : Type u} {S : Type u_4} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup S]
  [inst_3 : Module R M] [inst_4 : Module R S] [IsSemisimpleModule R M],
  IsIsotypicOfType R M S → ∃ ι, Nonempty (M ≃ₗ[R] ι →₀ S)

Defined in: Mathlib.RingTheory.SimpleModule.Isotypic
Cited by: 1 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup AddCommGroup Module Module IsSemisimpleModule

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setproof · 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
Ringstatement and proof · cited by 7,463
Submoduleproof · cited by 7,192
Set.Elemproof · cited by 7,166
Finsuppstatement and proof · cited by 5,255
LinearEquivstatement and proof · cited by 3,317
LinearEquiv.symmproof · cited by 1,461
DFinsuppproof · cited by 694
Nonempty.someproof · cited by 340

Cited by1

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IsIsotypic.linearEquiv_finsuppproof · cited by 0