Theorems · Theorem · ring theory
Module.End.IsSemisimple.mul_of_commute
∀ {M : Type u_2} [inst : AddCommGroup M] {K : Type u_3} [inst_1 : Field K] [inst_2 : Module K M] {f g : Module.End K M}
[FiniteDimensional K M] [PerfectField K], Commute f g → f.IsSemisimple → g.IsSemisimple → (f * g).IsSemisimple- Defined in
- Mathlib.LinearAlgebra.Semisimple
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 132 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
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.Endstatement and proof · cited by 774
- Commutestatement and proof · cited by 639
- MulMemClass.mul_memproof · cited by 173
- Algebra.subset_adjoinproof · cited by 109
- PerfectFieldstatement and proof · cited by 36
- Module.End.IsSemisimplestatement and proof · cited by 34
- Module.End.IsSemisimple.of_mem_adjoin_pairproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.