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Direct sum of modules — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Direct_sum_of_modules
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T16:14:39.087Z
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Direct sum of modules — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Direct_sum_of_modules (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_a90eaee5a403 (Metraipolis archive dc_a90eaee5a403, sha256 673c279a3061aa1d4f6e27ba4fa49a915d72279971d18a523529d9432a710af1)

BibTeX

@misc{dca90eaee5a403,
  title = {Direct sum of modules — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Direct_sum_of_modules},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_a90eaee5a403; sha256 673c279a3061aa1d4f6e27ba4fa49a915d72279971d18a523529d9432a710af1},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Direct_sum_of_modules. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Linear algebra»).
Fonte: Wikipedia in inglese, voce «Direct sum of modules» — https://en.wikipedia.org/wiki/Direct_sum_of_modules
Wikidata Q1142861 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1142861
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Direct_sum_of_modules?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1340697881, consultata il 2026-10-15T15:42:02.502Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: d56831389e5cb8ff2bc26f2cf949ba4bce7c7e16b522e58ee99e0a92c954cd67