On existence of canonical number system in certain classes of pure algebraic number fields
type: Item
instance of: scholarly article
zbMATH Open document ID: 1268.11147
author: Abdul Hameed
author: Toru Nakahara
author: Shahzad Ahmad
author: Syed Muhammad Husnine
publication date: 2012-08-06T00:00:00Z
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11R16
zbMATH DE Number: 6063551
zbMATH Keywords: monogenity
zbMATH Keywords: canonical number system
zbMATH Keywords: power integral basis
MaRDI profile type: Publication
title: On existence of canonical number system in certain classes of pure algebraic number fields
published in: The Journal of Prime Research in Mathematics
review text: The authors consider the existence of canonical number systems or equivalently monogenity of algebraic number fields. They prove that a canonical number system exists in a pure algebraic number field \(L=Q(\vartheta)\), where \(\vartheta\) is a root of the polynomial \(f(x)=x^{2^n}-m\), with a square free integer \(m\not = \pm 1\) and \(m\equiv 2,3\pmod 4\). Moreover, if \(L=Q(\vartheta)\), where \(\vartheta=\root n \of {m}\), with a square-free integer \(m\neq \pm 1\) and all prime factors of \(n\) divide \(m\), then \(L\) is monogenic and the minimal polynomial of \(\vartheta\) is a CNS polynomial.NEWLINENEWLINEThese important results will certainly have many application.
reviewed by: István Gaál
description: scientific article; zbMATH DE number 6063551