Direct Sum Of Modules

(Module Theory)

Tech

skills
Module Theory
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What is Direct sum of modules?

In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary" constraints, making it an example of a coproduct. Contrast with the direct product, which is the dual notion. The most familiar examples of this construction occur when considering vector spaces (modules over a field) and abelian groups (modules over the ring Z of integers). The construction may also be extended to cover Banach spaces and Hilbert spaces.

Technology Types

linear algebramodule theoryspacevector space

Synonyms

Complementary subspaceComplementary subspacesComplementary vector spaceOrthogonal direct sum

Translations

Batura zuzen (eu)Directe som (nl)Soma direta (pt)Somma diretta (it)Somme directe (fr)Suma directa (ca)Suma directa (es)Пряма сума (uk)Прямая сумма (ru)직합 (ko)加群の直和 (ja)

Tech Info


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