Abstract
Let β be a cyclotomic integer. The question of the solvability of the diophantine equation x q = 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 x q = β in a. J -field, or in other words whether β 1/q generates a. J -field.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
