A Ring of Pythagorean Triples over Quadratic Fields

• Date: 2014
• Main Authors: Harnchoowong, A., Somboonkulavudi, C., Гарнчоошонг, А., Сомбоонкулавуді, Ц.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2117
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 P η , sets of triples 〈α, β, γ〉 in P where η = γ − β. We show the ring structures of each P η and P from the ring structur...