Definitions
1.NounThe set of all possible tuples whose elements are elements of given, separately specified, sets."If A and B are sets, their direct product is the set of ordered pairs (a,b) with a in A and b in B."
2.NounSuch 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.NounSuch 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."A Boolean ring of order
2
n
{\displaystyle 2^{n}}
(or dimension
n
{\displaystyle n}
) may be constructed as the direct product of
n
{\displaystyle n}
Boolean rings of dimension one."
4.NounA topological space analogously formed from two or more (up to an infinite number of) topological spaces.
5.NounAny of a number of mathematical objects analogously derived from a given ordered set of objects.
6.NounA 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.