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Concept information

algebra > commutative algebra > commutative ring > Euclidean ring
... > algebra > abstract algebra > algebraic structure > ring theory > ring > commutative ring > Euclidean ring

Terme préférentiel

Euclidean ring  

Définition(s)

  • In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of integers. This generalized Euclidean algorithm can be put to many of the same uses as Euclid's original algorithm in the ring of integers: in any Euclidean domain, one can apply the Euclidean algorithm to compute the greatest common divisor of any two elements. In particular, the greatest common divisor of any two elements exists and can be written as a linear combination of them (Bézout's identity). Also every ideal in a Euclidean domain is principal, which implies a suitable generalization of the fundamental theorem of arithmetic: every Euclidean domain is a unique factorization domain.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Euclidean_domain)

Concept(s) générique(s)

Concept(s) associé(s)

Synonyme(s)

  • Euclidean domain

Traductions

URI

http://data.loterre.fr/ark:/67375/PSR-N6H408KW-V

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RDF/XML TURTLE JSON-LD Date de création 18/07/2023, dernière modif. 18/07/2023