 Krull-Schmidt decomposition (source code)

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= Krull-Schmidt decomposition
{c}
{title2=$X\cong\bigoplus_aM_a^{\oplus m_a}$}

A finite-dimensional <module> is $\bigoplus_aM_a^{\oplus m_a}$ with pairwise nonisomorphic indecomposables and uniquely determined multiplicities. The <Fitting lemma> makes their <endomorphism rings> local. The multiplicity spaces provide the general linear factors in the <Levi decomposition of a quiver automorphism group>.

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