Introduction

István Gaál
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István Gaál: University of Debrecen, Institute of Mathematics and Informatics

Chapter 1 in Diophantine Equations and Power Integral Bases, 2002, pp 1-5 from Springer

Abstract: Abstract Let K be an algebraic number field of degree n with ring of integers ℤ K . The ring ℤ K is called monogenic if it is a simple ring extension ℤ[α] of ℤ. In this case 1, α,...,αn-1 is an integral basis of K, called a power integral basis. Our main task is to develop algorithms for determining all generators α of power integral bases. As we shall see, this algorithmic problem is satisfactorily solved for lower degree number fields (especially for cubic and quartic fields) and there are efficient methods for certain classes of higher degree fields. Our algorithms enable us in many cases to describe all power integral bases also in infinite parametric families of certain number fields.

Keywords: Number Field; Diophantine Equation; Relative Index; Index Form; Algebraic Integer (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0085-7_1

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DOI: 10.1007/978-1-4612-0085-7_1

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