Theorems · Theorem · ring theory
Module.End.eq_zero_of_isNilpotent_of_isFinitelySemisimple
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{f : Module.End R M}, IsNilpotent f → f.IsFinitelySemisimple → f = 0- Defined in
- Mathlib.LinearAlgebra.Semisimple
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submoduleproof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.extproof · cited by 2,266
- map_zeroproof · cited by 1,614
- Submodule.spanproof · cited by 1,504
- Set.Iicproof · cited by 1,111
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.apply_eq_of_mem_of_comm_of_isFinitelySemisimple_of_isNilproof · cited by 2