Definition:Tensor Product of Abelian Groups/Family

Definition
Let $I$ be an indexing set.

Let $\family {G_i}_{i \mathop \in I}$ be a family of abelian groups.

Let $G = \ds \prod_{i \mathop \in I} G_i$ be their direct product.

Also see

 * Equivalence of Definitions of Tensor Product of Family of Abelian Groups

Special case

 * Definition:Tensor Product of Two Abelian Groups

Generalization

 * Definition:Tensor Product of Family of Modules