Definition:Direct Product of Vector Spaces/General Case

Definition
Let $K$ be a field.

Let $\family {V_i, +_i, \circ_i}_{i \mathop \in I}$ be a family of $K$-vector spaces.

The (external) direct product of $\family {V_i, +_i, \circ_i}_{i \mathop \in I}$ is their module direct product.