On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two

Autor:	Krishnamoorthy, Srilakshmi, Pasupulati, Sunil Kumar
Rok vydání:	2020
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	Lenstra introduced the notion of a Euclidean ideal class, which is a generalization of the Euclidean domain. Lenstra also proved that the Euclidean ideal in a number field $K$ implies that the class group of $K$ is cyclic. We construct a family of biquadratic fields with a Euclidean ideal whenever the class number is 2. This extends the families given by Graves, Hsu, Chattopadhyay, and Muthukrishnan. Comment: To appear in Archiv der Mathematik
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.06464 Zobrazit plný text záznamu View this record from Arxiv