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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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
- Mathematics Subject Classification (2000): 11R33, 11R23