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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. 1 Introduction This is a sequel to the previous papers [10, 11, 12, 13]. For a finite extension L/K of a number field K, it has a power integral basis (PIB for short) when OL = OK [#] for some # # OL . Here, OL... (Update)
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BibTeX entry: (Update)
H. Ichimura and H. Sumida. A note on integral bases of unramified cyclic extensions of prime degree. II. Manuscripta Math., 98:477--490, 1999. http://citeseer.ist.psu.edu/ichimura00note.html More
@misc{ ichimura99note,
author = "H. Ichimura and H. Sumida",
title = "A note on integral bases of unramified cyclic extensions of prime degree",
text = "H. Ichimura and H. Sumida. A note on integral bases of unramified cyclic
extensions of prime degree. II. Manuscripta Math., 98:477--490, 1999.",
year = "1999",
url = "citeseer.ist.psu.edu/ichimura00note.html" }
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[Article contains additional citations not shown here]
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