Let $R$ be a ring and ${M_i}{i\in I}$ a family of left $R$-modules indexed by $I$. The direct sum of the $M_i$, written \(\bigoplus_{i\in I} M_i,\) is the set of all sequences ${a_i}{i\in I}$ where $a_i \in M_i$ and $a_i=0$ for “cofinitely many” indices. That is, $a_i \neq 0$ for finitely many $i$.
Wikidata ID: Q1142861