Definition:Direct Product of Vector Spaces/General Case
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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.