Theorems · Definition · ring theory

Module.End.IsSemisimple

{R : Type u_1} →
  {M : Type u_2} → [inst : CommRing R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → Module.End R M → Prop

A linear endomorphism of an R-module M is called semisimple if the induced R[X]-module structure on M is semisimple. This is equivalent to saying that every f-invariant R-submodule of M has an f-invariant complement: see Module.End.isSemisimple_iff.

Defined in

Mathlib.LinearAlgebra.Semisimple

Cited by

34 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule