<abstract xmlns="http://www.w3.org/1999/xhtml"><p>For a prime <italic>p</italic>, we prove elementarily that the ring <bold>Z</bold>[√−5, 1/p] is Euclidean if and only if it is a PID iff <italic>p</italic> = 2 or <italic>p</italic> is congruent to 3 or 7 modulo 20.</p></abstract>

For a prime p, we prove elementarily that the ring Z[√−5, 1/p] is Euclidean if and only if it is a PID iff p = 2 or p is congruent to 3 or 7 modulo 20.

Euclidean Quotient Rings of <bold>Z</bold>[√−5]

Faculty of Mathematics and Informatics, University of Bucharest, 14 Academiei Str., Bucharest, RO 010014, Romania

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Euclidean Quotient Rings of Z[√−5]

Publié en ligne: 10 déc. 2014

Pages: 121 - 125

Reçu: 01 août 2013

Accepté: 01 sept. 2013

DOI: https://doi.org/10.2478/auom-2014-0010

Mots clés
Euclidean domain, PID

© 2014 Tiberiu Dumitrescu and Alexandru Gica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Euclidean Quotient Rings of Z[√−5]

Publié en ligne: 10 déc. 2014

Pages: 121 - 125

Reçu: 01 août 2013

Accepté: 01 sept. 2013

DOI: https://doi.org/10.2478/auom-2014-0010

Mots clésEuclidean domain, PID

© 2014 Tiberiu Dumitrescu and Alexandru Gica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Euclidean domain, PID