Definition:Free Module on Set

Definition
Let $R$ be a ring.

Let $I$ be an indexing set.

The direct sum:


 * $\displaystyle R^{\left({I}\right)} := \bigoplus_{i \mathop \in I} R$

is called the free $R$-module indexed by $I$.

Also see

 * Universal Property of Free Module Indexed by Set
 * Free Module Indexed by Set is Free