Definition:Free Module on Set

Definition
Let $R$ be a ring.

Let $I$ be an indexing set.

The free $R$-module on $I$ is the direct sum of $R$ as a module over itself:
 * $\ds R^{\paren I} := \bigoplus_{i \mathop \in I} R$

of the family $I \to \set R$ to the singleton $\set R$.

Also see

 * Universal Property of Free Module on Set
 * Free Module on Set is Free

Special case

 * Definition:Free Abelian Group on Set