\(N\) – real fields
A field F is n-real if -1 is not the sum of n squares in F. It is shown that a field F is m-real if and only if rank ( \(AA^t\) ) = rank (A) for every n × m matrix A with entries from F. An n-real field F is n-real closed if every proper algebraic extension of F is not n-real. It is shown that if a...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/961 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-9612018-05-13T10:43:19Z \(N\) – real fields Feigelstock, Shalom \(n\)-real, \(n\)-real closed 12D15 A field F is n-real if -1 is not the sum of n squares in F. It is shown that a field F is m-real if and only if rank ( \(AA^t\) ) = rank (A) for every n × m matrix A with entries from F. An n-real field F is n-real closed if every proper algebraic extension of F is not n-real. It is shown that if a 3-real field F is 2-real closed, then F is a real closed field. For F a quadratic extension of the field of rational numbers, the greatest integer n such that F is n-real is determined. Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/961 Algebra and Discrete Mathematics; Vol 2, No 3 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/961/490 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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2018-05-13T10:43:19Z |
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OJS |
| language |
English |
| topic |
\(n\)-real \(n\)-real closed 12D15 |
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\(n\)-real \(n\)-real closed 12D15 Feigelstock, Shalom \(N\) – real fields |
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\(n\)-real \(n\)-real closed 12D15 |
| format |
Article |
| author |
Feigelstock, Shalom |
| author_facet |
Feigelstock, Shalom |
| author_sort |
Feigelstock, Shalom |
| title |
\(N\) – real fields |
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\(N\) – real fields |
| title_full |
\(N\) – real fields |
| title_fullStr |
\(N\) – real fields |
| title_full_unstemmed |
\(N\) – real fields |
| title_sort |
\(n\) – real fields |
| description |
A field F is n-real if -1 is not the sum of n squares in F. It is shown that a field F is m-real if and only if rank ( \(AA^t\) ) = rank (A) for every n × m matrix A with entries from F. An n-real field F is n-real closed if every proper algebraic extension of F is not n-real. It is shown that if a 3-real field F is 2-real closed, then F is a real closed field. For F a quadratic extension of the field of rational numbers, the greatest integer n such that F is n-real is determined. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/961 |
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AT feigelstockshalom nrealfields |
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2025-12-02T15:43:42Z |
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2025-12-02T15:43:42Z |
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