direct product

Meanings

1. The set of all possible tuples whose elements are elements of given, separately specified, sets.
2. Such a set of tuples formed from two or more groups, forming another group whose group operation is the component-wise application of the original group operations and of which the original groups are normal subgroups.
3. Such a set of tuples formed from two or more rings, forming another ring whose operations arise from the component-wise application of the corresponding original ring operations.
4. A topological space analogously formed from two or more (up to an infinite number of) topological spaces.
5. Any of a number of mathematical objects analogously derived from a given ordered set of objects.
6. A high-level generalization of the preceding that applies to objects in an arbitrary category and produces a new object constructable by morphisms from each of the original objects.

Translations