direct sum
noun Date: circa 1928 Cartesian productcompare direct product

New Collegiate Dictionary. 2001.

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  • 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 — noun a union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets (Freq. 1) • Hypernyms: ↑union, ↑sum, ↑join * * * noun : cartesian product herein * * * Math. a composi …   Useful english dictionary

  • direct sum — Math. a composition of two disjoint sets, as vector spaces, such that every element in the composition can be written uniquely as the sum of two elements, one from each of the given sets. [1925 30] * * * …   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 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

  • Direct sum of permutations — In combinatorial mathematics, the direct sum of the permutation π of length m and the permutation σ of length n is the permutation of length m + n defined by See also Skew sum of permutations Categories: Mathematics stubsPermutations …   Wikipedia

  • Sum (disambiguation) — Sum usually refers to summation.It may also refer to: *Sum (category theory), also referred to as coproduct *Sum (country subdivision), an administrative division used in Mongolia and nearby regions *SUM (interbank network) *Soccer United… …   Wikipedia

  • Direct — may refer to: Direct current, a direct flow of electricity Direct examination, the in trial questioning of a witness by the party who has called him or her to testify Direct sum of modules, a construction in abstract algebra which combines… …   Wikipedia

  • 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

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