Abstract.
Integral bases of cyclotomic fields are constructed that allow to determine easily the smallest cyclotomic field in which a given sum of roots of unity lies. For subfields of cyclotomic fields integral bases are constructed that consist of orbit sums of Galois groups on roots of unity. These bases are closely related to the bases of the enveloping cyclotomic fields mentioned above. In both situations bases over the rationals and over cyclotomic fields are treated.
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Received: March 22, 1995; revised version: July 3, 1996
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Breuer, T. Integral Bases for Subfields of Cyclotomic Fields. AAECC 8, 279–289 (1997). https://doi.org/10.1007/s002000050065
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DOI: https://doi.org/10.1007/s002000050065