Journal of Prime Research in Mathematics
Vol. 1 (2011), Issue 1, pp. 19 – 24
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
On existence of canonical number system in certain classes of pure algebraic number fields
Abdul Hameed
National University of Computer & Emerging Sciences, Lahore Campus, Lahore, Pakistan.
Toru Nakahara
National University of Computer & Emerging Sciences, Peshawar Campus, Peshawar, Pakistan.
Syed Muhammad Husnine
National University of Computer & Emerging Sciences, Lahore Campus, Lahore, Pakistan.
Shahzad Ahmad
National University of Computer & Emerging Sciences, Lahore Campus, Lahore, Pakistan.
\(^{1}\)Corresponding Author: abdul.hameed@lhr.nu.edu.pk
Copyright © 2011 Abdul Hameed, Toru Nakahara, Syed Muhammad Husnine, Shahzad Ahmad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: December, 2011.
Abstract
Canonical Number System can be considered as natural generalization of radix representation of rational integers to algebraic integers. We determine the existence of Canonical Number System in two classes of pure algebraic number fields of degree \(2^n\) and \(n\).
Keywords:
CNS, Eisenstein polynomial, discriminant and index of an algebraic integer, field discriminant, monogeneity.