Characterisation of the numbers which satisfy the height reducing property
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Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
Let α be a complex number. We show that there is a finite subset F of the ring of the rational integers
Z, such that F [α] = Z[α], if and only if α is an algebraic number whose conjugates, over the field of
the rationals, are all of modulus one, or all of modulus greater than one. This completes the answer to a
question, on the numbers satisfying the height reducing property, posed in Akiyama and Za¨ımi (2013).
⃝c 2014 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved
Description
Keywords
Height of polynomials, Special algebraic numbers, Representations of algebraic numbers