Direct product

In mathematics, the direct product of a collection of algebraic structures (such as groups, rings, or vector spaces) is a structure of the same type constructed by combining the given structures in a specific way, described below. Its underlying set is the Cartesian product of the underlying sets of the given structures.

The direct sum of a collection of structures agrees with the direct product in some but not all cases. A direct product is an example of a product in a category, whereas a direct sum is an example of a coproduct.

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