For example, if A and B are sets, their direct product is the set of pairs (a,b) with a in A and b in B.
Wikipedia foundation.
Direct product — In mathematics, one can often define a direct product of objects already known, giving a new one. This is generally the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one… … Wikipedia
Direct product of groups — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product … Wikipedia
direct product — I. noun : scalar product II. noun : cartesian product herein ; especially : a group that is the Cartesian product of two other groups * * * Math. a group, or other such system, every element of which can be written uniquely as the … Useful english dictionary
direct product — noun Date: circa 1925 Cartesian product; especially a group that is the Cartesian product of two other groups … New Collegiate Dictionary
direct product — Math. a group, or other such system, every element of which can be written uniquely as the product of elements of disjoint groups, with each group contributing one element to the product. [1920 25] * * * … Universalium
Direct sum of modules — For the broader use of the term in mathematics, see Direct sum. In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The result of the direct summation of modules is the smallest general… … Wikipedia
Direct sum — The symbol denotes direct sum; it is also the astrological and astronomical symbol for Earth, and a symbol for the Exclusive disjunction. In mathematics, one can often define a direct sum of objects already known, giving a new one. This is… … Wikipedia
Direct sum of groups — In mathematics, a group G is called the direct sum of a set of subgroups {Hi} if each Hi is a normal subgroup of G each distinct pair of subgroups has trivial intersection, and G = <{Hi}>; in other words, G is generated by the subgroups… … Wikipedia
Product of rings — In mathematics, it is possible to combine several rings into one large product ring. This is done as follows: if I is some index set and Ri is a ring for every i in I, then the cartesian product Πi in I Ri can be turned into a ring by defining… … Wikipedia
Product (category theory) — In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct… … Wikipedia
