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Quotient ring — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Quotient_ring
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-31T14:38:16.532Z
SHA-256 of the archived text: 170401560908b91442baa33198f224d1e8b94c2ecf49b242b91c701d39de83ca
Stable URL of this page: https://metraipolis.com/documento/dc_799e893af7df

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Quotient ring — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Quotient_ring (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_799e893af7df (Metraipolis archive dc_799e893af7df, sha256 170401560908b91442baa33198f224d1e8b94c2ecf49b242b91c701d39de83ca)

BibTeX

@misc{dc799e893af7df,
  title = {Quotient ring — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Quotient_ring},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_799e893af7df; sha256 170401560908b91442baa33198f224d1e8b94c2ecf49b242b91c701d39de83ca},
  year = {2026}
}

Archived text

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

In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting of universal algebra. Starting with a ring R {\displaystyle R} and a two-sided ideal I {\displaystyle I} in R {\displaystyle R} , a new ring, the quotient ring R / I {\displaystyle R\ /\ I} , is constructed, whose elements are the cosets of I {\displaystyle I} in R {\displaystyle R} subject to + {\displaystyle +} and ⋅ {\displaystyle \cdot } operations compatible with + {\displaystyle +} and ⋅ {\displaystyle \cdot } in R {\displaystyle R} . Quotient rings are denoted as a fraction, usually using the fraction slash " / {\displaystyle /} " as the separator. The alternative of stacking the ring over the ideal using a horizontal line (i.e., the fraction bar) as a separator is sometimes used if the expressions for the ring or the ideal are long or cumbersome. Quotient rings are distinct from the "quotient field", or field of fractions, of an integral domain as well as from the more general "rings of quotients" obtained by localization.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «linear algebra»).
Fonte: Wikipedia in inglese, voce «Quotient ring» — https://en.wikipedia.org/wiki/Quotient_ring
Wikidata Q619436 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q619436
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Quotient_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 1366975432, consultata il 2026-10-31T14:27:46.049Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 7f20624b32774a4a84f7bee4d96bf0e351af9b2b7a9b0a2d4ed2713e938ffd1f