Theorems · Theorem · ring theory

Module.End.eq_zero_of_isNilpotent_isSemisimple

∀ {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.IsSemisimple → f = 0

Defined in: Mathlib.LinearAlgebra.Semisimple
Cited by: 1 results in Mathlib
Foundations: Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites16

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
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Polynomialproof · cited by 5,681
Idealproof · cited by 4,748
Polynomial.Xproof · cited by 1,639
Module.Endstatement and proof · cited by 774
IsNilpotentstatement and proof · cited by 248
Polynomial.aeval_Xproof · cited by 120
RingHom.mem_kerproof · cited by 49
Module.End.IsSemisimplestatement and proof · cited by 34

Cited by1

Results whose statement or proof uses this declaration.

Module.End.eq_zero_of_isNilpotent_of_isFinitelySemisimpleproof · cited by 1