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J-fields generated by roots of cyclotomic integers

Published online by Cambridge University Press:  26 February 2010

Veikko Ennola
Veikko Ennola
Affiliation:
Department of Mathematics, University of Turku, SF–2O50O Turku 50, Finland
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Let β be a cyclotomic integer. The question of the solvability of the diophantine equation xq = β in a cyclotomic field has been considered by many authors (see [4], [5], [12]). Some of the methods used in these investigations also work in J-fields. (As to the definition, see Section 2.) It is well known that J-fields share some important properties with cyclotomic fields. It is also easy to give interesting examples where the solution belongs to a. J-field but not to a cyclotomic field. It seems therefore to be of some importance to consider in general the solvability of xq = β in a. J-field, or in other words whether β1/q generates a. J-field.

Type
Research Article
Information
Mathematika , Volume 25 , Issue 2 , December 1978 , pp. 242 - 250
Copyright
Copyright © University College London 1978

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