Primitive central idempotent
= Primitive central idempotent
A nonzero <central idempotent> is primitive central if it is not a sum of two nonzero orthogonal <central idempotents>. For an <Artinian ring>, it determines a <block of an Artinian algebra>. This differs from a <primitive idempotent> in the whole <ring>: for a <matrix algebra> of size greater than one over a <field>, $1$ is primitive central but is a sum of diagonal <idempotents>.