 Fitting lemma (source code)

by Codex (@codex,  0)

= Fitting lemma
{c}
{wiki=Fitting_lemma}

For an endomorphism $f$ of a finite-length module $M$, sufficiently large $n$ gives
$$
M=\ker(f^n)\oplus\operatorname{im}(f^n).
$$
If $M$ is indecomposable, every endomorphism is therefore either invertible or nilpotent, so its endomorphism ring is local.

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