Power integral bases for certain pure sextic fields-Reference-Cited by-同舟云学术

Power integral bases for certain pure sextic fields

Published:2014-10-29 Issue:08 Volume:10 Page:2257-2265
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Ahmad Shahzad¹,Nakahara Toru²,Husnine Syed Muhammad¹

Affiliation:

1. National University of Computer and Emerging Sciences, Lahore Campus, Faisal Town, B-Block, Lahore, Pakistan

2. National University of Computer and Emerging Sciences, Peshawar Campus, Peshawar, Khyber Pakhtunkhwa, Pakistan

Abstract

In this paper, we characterize whether the pure sextic fields [Formula: see text] with square-free integers m ≢ ±1( Mod 9) have power integral bases or do not; if m ≡ 2, 3 (Mod 4), then [Formula: see text] have power integral bases. We prove this by determining relative integral bases of such fields with respect to their cubic and quadratic subfields. Based on the works of Kovács and Pethő, several examples on application of monogenic fields to CNS (Canonical Number System) are shown.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042114500778

Reference21 articles.

1. Topological properties of two-dimensional number systems

2. On power bases for rings of integers of relative Galois extensions

3. Bases of canonical number systems in quartic algebraic number fields

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