= Block of an Artinian algebra
= Blocks of an Artinian algebra
{synonym}
A block of an <associative algebra> with a finite decomposition of its identity is a two-sided <direct summand> $Ae$ corresponding to a <primitive central idempotent> $e$. Its identity is $e$, and it cannot be split into two nonzero <algebras> by <central idempotents>. For a <group algebra> of a finite <group>, this agrees with a <block of a group algebra>. Orthogonal <primitive central idempotents> give $A=\bigoplus_iAe_i$.
Back to article page
