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Mathematica Slovaca

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Volume 60, Issue 6


On correspondence between orders and ideals with a normal basis in cyclic subfields of Q(ξp) of a prime degree l

Juraj Kostra
Published Online: 2010-12-12 | DOI: https://doi.org/10.2478/s12175-010-0046-2


Let K be a tamely ramified cyclic algebraic number field of prime degree l. In the paper one-to-one correspondence between all orders of K with a normal basis and all ideals of K with a normal basis is given.

MSC: Primary 11R16; Secondary 11C20

Keywords: order; normal basis; ambiguous ideal; circulant matrix

  • [1] JAKUBEC, S. —KOSTRA, J.: A note on normal bases of ideals, Math. Slovaca 42 (1992), 677–684. Web of ScienceGoogle Scholar

  • [2] LEOPOLD, H.: Zur arithmetic in abelschen zahlkorpen, J. Reine Angew. Math. 209 (1962), 54–71. Google Scholar

  • [3] ULLOM, S.: Normal bases in Galois extensions of number fields, Nagoya Math. J. 34 (1969), 153–167. Google Scholar

About the article

Published Online: 2010-12-12

Published in Print: 2010-12-01

Citation Information: Mathematica Slovaca, Volume 60, Issue 6, Pages 787–792, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-010-0046-2.

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© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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