Akiyama, ShigekiThuswaldner, J¨org M.Zaimi, Toufik2022-04-272022-04-272012http://hdl.handle.net/123456789/12967Let 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 reservedenHeight of polynomialsSpecial algebraic numbersRepresentations of algebraic numbersArticle