Let be the following definition of product of an associative algebra $$e_{i}e_{j}={\sum}c_{ij}^{k}e_{k}$$ Is it safe to say that being an element $a= {\sum}a^{k}e_{k}$, $a$ is idempotent if and only if $$c_{ij}^{k}a^{i}a^{j}=a^{k},$$ for all $1\leq i,\,j,\,k\leq n$? It seems trivial to me but since I didn't find it anywhere I'm worried I miseyed something. Thanks
2026-04-09 15:59:35.1775750375
Idempotents element from structure constants associative algebra
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