Back Suma directa Catalan Direkte Summe German Suma directa de módulos Spanish Batura zuzen Basque Modulien suora summa Finnish Somme directe French סכום ישר HE Somma diretta Italian 加群の直和 Japanese 직합 Korean
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.
See the article decomposition of a module for a way to write a module as a direct sum of submodules.