caa a22 4500 445869119 CHVBK 20180317145506.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00605-009-0162-7 doi (NATIONALLICENCE)springer-10.1007/s00605-009-0162-7 Widmer Martin Department of Mathematics, University of Texas at Austin, 1 University Station C1200, 78712, Austin, TX, USA aut On certain infinite extensions of the rationals with Northcott property [Elektronische Daten] [Martin Widmer] A set of algebraic numbers has the Northcott property if each of its subsets of bounded Weil height is finite. Northcott's Theorem, which has many Diophantine applications, states that sets of bounded degree have the Northcott property. Bombieri, Dvornicich and Zannier raised the problem of finding fields of infinite degree with this property. Bombieri and Zannier have shown that $${{\mathbb Q}_{ab}^{(d)}}$$ , the maximal abelian subfield of the field generated by all algebraic numbers of degree at most d, is such a field. In this note we give a simple criterion for the Northcott property and, as an application, we deduce several new examples, e.g. $${{\mathbb Q}(2^{1/d_1},3^{1/d_2},5^{1/d_3},7^{1/d_4},11^{1/d_5},\ldots)}$$ has the Northcott property if and only if $${2^{1/d_1}, 3^{1/d_2}, 5^{1/d_3}, 7^{1/d_4}, 11^{1/d_5}}$$ , . . . tends to infinity. Springer-Verlag, 2009 Northcott property nationallicence Height nationallicence Preperiodic points nationallicence Field arithmetic nationallicence Monatshefte für Mathematik Springer Vienna 162/3(2011-03-01), 341-353 0026-9255 162:3<341 2011 162 605 https://doi.org/10.1007/s00605-009-0162-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-009-0162-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Widmer Martin Department of Mathematics, University of Texas at Austin, 1 University Station C1200, 78712, Austin, TX, USA aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 162/3(2011-03-01), 341-353 0026-9255 162:3<341 2011 162 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer