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A note on integral bases of unramified cyclic extensions of prime degree. II

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Abstract:

Let p be a prime number and K a number field containing a primitive p-th root of unity. It is known that an unramified cyclic extension L/K of degree p has a power integral basis if it has a normal integral basis. We show that for all p, the converse is not true in general.

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Authors and Affiliations

  1. Department of Mathematics, Yokohama City University, 22–2, Seto, Kanazawa-ku, Yokohama, 236-0027, Japan. e-mail: ichimura@math.yokohama-cu.ac.jp, , , , , , JP

    Humio Ichimura

  2. Faculty of Integrated Arts and Sciences, Hiroshima University, Kagamiyama, Higashi–Hiroshima, 739-8521, Japan. e-mail: sumida@mis.hiroshima-u.ac.jp, , , , , , JP

    Hiroki Sumida

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  1. Humio Ichimura
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  2. Hiroki Sumida
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Received: 18 July 2000 / Revised version: 18 October 2000

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Ichimura, H., Sumida, H. A note on integral bases of unramified cyclic extensions of prime degree. II. manuscripta math. 104, 201–210 (2001). https://doi.org/10.1007/s002290170039

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  • DOI: https://doi.org/10.1007/s002290170039

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