IJPAM: Volume 16, No. 2 (2004)

ON THE STRUCTURE OF THE RING $\mathbb{Z}\left[\sqrt[3]{2}\right]$

Bram van Asch
Department of Mathematics and Computing Science
Eindhoven University of Technology
P.O. Box 513, 5600 MB Eindhoven, THE NETHERLANDS
e-mail: a.g.v.asch@tue.nl

Abstract.It has been known for some time that the ring $\mathbb{Z}\left[\sqrt[3]{2}\right]$ is Euclidean. The first one to prove this fact in a general setting was H.J. Godwin (see [#!Godwin!#]). In this note we present an explicit description of the Euclidean algorithm in this ring. Besides, all primes in $\mathbb{Z}\left[\sqrt[3]{2}\right]$ are determined.

Received: August 12, 2004

AMS Subject Classification: 11R04, 11R16, 11R27

Key Words and Phrases: ring of integers, division algorithm, prime

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 2