Noun
(set theory) The 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.
(group theory) 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.
(ring theory) 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.
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.
(topology) A topological space analogously formed from two or more (up to an infinite number of) topological spaces.
(mathematics) Any of a number of mathematical objects analogously derived from a given ordered set of objects.
(category theory) 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.
Source: en.wiktionary.orgAcross professions, consistency is a direct product of work ethic. Harsha Bhogle
The universe is an enormous direct product of representations of symmetry groups. Steven Weinberg
A "finite" direct product may also be viewed as a direct sum of ideals. Source: Internet
Direct product and direct sum main The direct product of vector spaces and the direct sum of vector spaces are two ways of combining an indexed family of vector spaces into a new vector space. Source: Internet
For example, the Schur–Zassenhaus theorem implies the existence of a semi-direct product among groups of order 6; there are two such products, one of which is a direct product, and the other a dihedral group. Source: Internet
CDRH also conducts limited amounts of direct product testing. Source: Internet