# Direct Sum Of Modules

Tech

## 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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— Date merged: 11/6/2021, 1:32:51 PM
— Date scraped: 5/20/2021, 6:16:34 PM