Theorems · Theorem · ring theory

Module.End.IsSemisimple.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}, f.IsSemisimple → f.IsFinitelySemisimple

Defined in: Mathlib.LinearAlgebra.Semisimple
Cited by: 4 results in Mathlib
Foundations: Depth 129 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.

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
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Submoduleproof · cited by 7,192
Module.Finiteproof · cited by 1,032
Module.Endstatement and proof · cited by 774
Module.End.invtSubmoduleproof · cited by 93
Module.End.IsSemisimplestatement and proof · cited by 34
Module.End.IsFinitelySemisimplestatement · cited by 12
Module.End.isFinitelySemisimple_iff'proof · cited by 1
Module.End.IsSemisimple.restrictproof · cited by 1

Cited by4

Results whose statement or proof uses this declaration.

LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpaceproof · cited by 8
LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebraproof · cited by 1
Module.End.isFinitelySemisimple_iff_isSemisimpleproof · cited by 1
Module.End.IsSemisimple.iSup_maxGenEigenspace_eq_top_iffproof · cited by 0