**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** — noun Date: circa 1928 Cartesian product compare direct product … New Collegiate Dictionary

**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