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Existence of relative integral basis over quadratic fields and Pólya property

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Abstract

For \(L/K\) a finite extension of algebraic number fields, L may or may not have a relative integral basis over K. We show the existence of relative integral basis of a biquadratic field \(L=\mathbb{Q}(\sqrt{m},\sqrt{n})\) over its quadratic subfield \(K=\mathbb{Q}(\sqrt{m})\) is equivalent to that K is a Pólya field, or equivalently all strongly ambiguous ideal classes of K are trivial.

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Acknowledgement

The author would like to thank the anonymous referee for many useful comments and suggestions.

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  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5746, Tehran, Iran

    A. Maarefparvar

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  1. A. Maarefparvar
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Correspondence to A. Maarefparvar.

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This research was supported by a grant from IPM.

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Maarefparvar, A. Existence of relative integral basis over quadratic fields and Pólya property. Acta Math. Hungar. 164, 593–598 (2021). https://doi.org/10.1007/s10474-021-01158-2

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  • DOI: https://doi.org/10.1007/s10474-021-01158-2

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