# direct sum

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## direct sum

[də¦rekt ′səm]
(mathematics)
If each of the sets in a finite direct product of sets has a group structure, this structure may be imposed on the direct product by defining the composition “componentwise”; the resulting group is called the direct sum.
References in periodicals archive ?
1 and 2] give recurrences that reduce the computation of the Mobius function [mu]([sigma], [tau]) to Mobius function calculations of the form [mu]([sigma]', [tau]') where [tau]' is a single component of [tau] and [sigma]' is a direct sum of consecutive components of [sigma].
The tangent space has the direct sum decomposition into subbundles:
explores advanced topics in direct sum decompositions of abelian groups and their consequences.
presents an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization.
We define their direct sum M [direct sum] M' on the ground set E [?
If V is a direct sum of irreducible kG-submodules, then we call V (as well as G and [phi]) completely reducible.
q]-connection on a left U-module E, [pi] is the projection on the first summand in the direct sum M [direct sum] N, and [pi]([omega] [[cross product].
Although every direct summand of a [pi]-Rickart module is [pi]-Rickart, we give an example to show that a direct sum of [pi]-Rickart modules need not be [pi]-Rickart.
Let X, Y [subset] V be two subspaces of a vector space V such that X [intersection] Y = {0}, then their direct sum is denoted by X [direct sum] Y.
Assume that J has a local linking at 0 with respect to a direct sum decomposition H = [H.
We show that such a polytope is lattice equivalent to a direct sum of del Pezzo polytopes, pseudo del Pezzo polytopes, or a (possibly skew) bipyramid over (pseudo) del Pezzo polytopes.

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