= Block of a finite-dimensional algebra
{title2=$Re$}
A block of a finite-dimensional <associative algebra> $R$ is a two-sided ideal $Re$ associated with a <primitive idempotent> $e$ in the <center of an associative algebra>. Its identity is $e$, and $R$ is the product of these blocks. An $R$-<module> belongs to this block if $eM=M$. For a <semisimple algebra>, the <Artin–Wedderburn theorem> says the blocks are its full <matrix algebras> over division rings. For a <group algebra> this specializes to a <block of a group algebra>.
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