- direct product
- noun Date: circa 1925 Cartesian product; especially a group that is the Cartesian product of two other groups
New Collegiate Dictionary. 2001.
direct product
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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 — noun a) The direct product of an indexed family of sets is the set of functions from the indexing set to the union of the family, whose values at any given index lie in the set indexed thereby. For example, if A and B are sets, their direct… … Wiktionary
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 — 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
