Normal integral bases of ∞ -ramified abelian extensions of totally real number fields |
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| Authors: | Fuminori Kawamoto Yoshitaka Odai |
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| Institution: | 1. Department of Mathematics, Faculty of Science, Gakushuin University, 1-5-1 Mejiro Toshima-ku, 171-8588, Tokyo, Japan
2. Faculty of Humanities and Social Sciences, Iwate University, 3-18-34 Ueda, 020-8550, Morioka, Japan
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| Abstract: | LetF be a totally real number field and a product of some real primes ofF. J. Brinkhuis gave a necessary condition for a finite abelian extension ofF which is unramified outside to have a normal integral basis. We consider the converse of his result and give a necessary and sufficient condition. Furthermore, we concretely express it whenF is a real quadratic field or a cyclic cubic field. |
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