Nagoya Mathematical Journal

Monogenesis of the rings of integers in certain imaginary abelian fields

Toru Nakahara and Syed Inayat Ali Shah

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In this paper we consider a subfield $K$ in a cyclotomic field $k_m$ of conductor $m$ such that $\left[k_m : K\right] = 2$ in the cases of $m = \ell p^n$ with a prime $p,$ where $\ell = 4$ or $p > \ell = 3.$ Then the theme is to know whether the ring of integers in $K$ has a power basis or does not.

Article information

Nagoya Math. J., Volume 168 (2002), 85-92.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R18: Cyclotomic extensions
Secondary: 11R04: Algebraic numbers; rings of algebraic integers


Shah, Syed Inayat Ali; Nakahara, Toru. Monogenesis of the rings of integers in certain imaginary abelian fields. Nagoya Math. J. 168 (2002), 85--92.

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