Theorems · Theorem · ring theory
Module.End.isSemisimple_of_squarefree_aeval_eq_zero
∀ {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}
{p : Polynomial K}, Squarefree p → (Polynomial.aeval f) p = 0 → f.IsSemisimple- Defined in
- Mathlib.LinearAlgebra.Semisimple
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupFieldModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapproof · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Idealproof · cited by 4,748
- AlgHomstatement · cited by 3,236
- AddMonoidHomproof · cited by 3,230
- HasQuotient.Quotientproof · cited by 2,301
- FiniteDimensionalproof · cited by 1,854
Cited by4
Results whose statement or proof uses this declaration.
- Module.End.IsSemisimple.of_mem_adjoin_pairproof · cited by 3
- Module.End.exists_isNilpotent_isSemisimple_of_separable_of_dvd_powproof · cited by 1
- LieAlgebra.ad_isSemisimple_of_isSemisimpleproof · cited by 1
- Module.End.IsSemisimple.aevalproof · cited by 1