On number fields without a unit primitive element (Q2814341)
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scientific article; zbMATH DE number 6595981
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On number fields without a unit primitive element |
scientific article; zbMATH DE number 6595981 |
Statements
21 June 2016
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primitive elements
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Pisot numbers
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units
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CM-fields
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reciprocal integers
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On number fields without a unit primitive element (English)
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In this paper, the authors give necessary and sufficient conditions when a number field \(K\) is generated by a unit. This happens when (i) \(K\) is not a CM-field, or (ii) \(K\) is a CM-field and contains a non-real root of unity, or (iii) \(K\) is a CM-field which does not contain a non-real root of unity and is generated by \(\sqrt{-\beta}\), where \(\beta\) is a totally positive Pisot unit. Some families of number fields without a unit generator are given and several related questions are also considered.
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