Browsing by Author "Akiyama, Shigeki"

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    Characterisation of the numbers which satisfy the height reducing property
    (Elsevier, 2012) Akiyama, Shigeki; Thuswaldner, J¨org M.; Zaimi, Toufik
    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