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arXiv · 1305.6781

Generators for abelian extensions of number fields

Ja Kyung Koo·Dong Hwa Shin
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Abstract

Let $U/L$ be a finite abelian extension of number fields. We first construct a universal primitive generator of $U$ over $L$ whose relative trace to any intermediate field $F$ becomes a generator of $F$ over $L$, too. We also develop a similar argument in terms of norm. As its examples we investigate towers of ray class fields over imaginary quadratic fields. And, we further present a new method of finding a normal element for the extension $U/L$.

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Ja Kyung Koo, Dong Hwa Shin. 2013-05-29. Generators for abelian extensions of number fields. https://arxiv.org/abs/1305.6781

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