A ring of Pythagorean triples over quadratic fields

• Published in: Український математичний журнал
• Date: 2014
• Main Authors: Somboonkulavudi, C., Harnchoowong, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2014
• Subjects: Короткі повідомлення
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/165128
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A ring of Pythagorean triples over quadratic fields / C. Somboonkulavudi, A. Harnchoowong // Український математичний журнал. — 2014. — Т. 66, № 1. — С. 135–139. — Бібліогр.: 2 назв. — англ.

Let K be a quadratic field and let R be the ring of integers of K such that R is a unique factorization domain. The set P of all Pythagorean triples in R is partitioned into Pη , sets of triples 〈α, β, γ〉 in P where η = γ − β. We show the ring structures of each Pη and P from the ring structure of R...