Direct product

In mathematics, one can often define a direct product of objects already known, giving a new one. This generalizes the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one talks about the product in category theory, which formalizes these notions.

Examples are the product of sets, groups (described below), rings, and other algebraic structures. The product of topological spaces is another instance.[dubious ]

There is also the direct sum – in some areas this is used interchangeably, while in others it is a different concept.

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