Theorems · Theorem · ring theory
Module.End.IsSemisimple.of_mem_adjoin_singleton
∀ {M : Type u_2} [inst : AddCommGroup M] {K : Type u_3} [inst_1 : Field K] [inst_2 : Module K M] {f : Module.End K M}
[FiniteDimensional K M], f.IsSemisimple → ∀ {a : Module.End K M}, a ∈ K[f] → a.IsSemisimple- Defined in
- Mathlib.LinearAlgebra.Semisimple
- Cited by
- 1 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- FiniteDimensionalstatement and proof · cited by 1,854
- Subalgebrastatement and proof · cited by 1,353
- Module.Endstatement and proof · cited by 774
- Polynomial.aevalproof · cited by 615
- Algebra.adjoinstatement and proof · cited by 535
- AlgHom.toRingHomproof · cited by 490
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.IsSemisimple.powproof · cited by 0