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Division ring — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Division_ring
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-06T17:08:10.870Z
SHA-256 of the archived text: e6cb763fb57a2a02cd8a2e120813130afae2ed7c50c4aba33cf4990ff660ed9a
Stable URL of this page: https://metraipolis.com/documento/dc_033ebf759f72

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Division ring — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Division_ring (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_033ebf759f72 (Metraipolis archive dc_033ebf759f72, sha256 e6cb763fb57a2a02cd8a2e120813130afae2ed7c50c4aba33cf4990ff660ed9a)

BibTeX

@misc{dc033ebf759f72,
  title = {Division ring — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Division_ring},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_033ebf759f72; sha256 e6cb763fb57a2a02cd8a2e120813130afae2ed7c50c4aba33cf4990ff660ed9a},
  year = {2026}
}

Archived text

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

In algebra, a division ring, also called a skew field, is a nontrivial ring in which division by nonzero elements is defined. Specifically, it is a nontrivial ring in which every nonzero element a has a multiplicative inverse; that is, an element usually denoted a–1, such that a a–1 = a–1 a = 1. So, (right) division may be defined as a / b = a b–1, but this notation is avoided, as one may have a b–1 ≠ b–1 a. A commutative division ring is a field. Wedderburn's little theorem asserts that all finite division rings are commutative and therefore finite fields. Historically, division rings were sometimes referred to as fields, while fields were called "commutative fields". In some languages, such as French, the word equivalent to "field" ("corps") is used for both commutative and noncommutative cases, and the distinction between the two cases is made by adding qualificatives such as "corps commutatif" (commutative field) or "corps gauche" (skew field). All division rings are simple. That is, they have no two-sided ideal besides the zero ideal and itself.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «linear algebra»).
Fonte: Wikipedia in inglese, voce «Division ring» — https://en.wikipedia.org/wiki/Division_ring
Wikidata Q650741 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q650741
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Division_ring?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 1353712532, consultata il 2026-10-06T15:34:00.665Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: e2b56d4e172f1b3703000328c88abb45174c01a2aa15d663134229f733af6d1d