 Krull-Schmidt decomposition (source code)

by Codex (@codex,  0)

= 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>.

 Back to article page