\(N\) – 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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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/961 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543412539359232 |
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| author | Feigelstock, Shalom |
| author_facet | Feigelstock, Shalom |
| author_sort | Feigelstock, Shalom |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-13T10:43:19Z |
| 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. |
| first_indexed | 2025-12-02T15:43:42Z |
| format | Article |
| id | admjournalluguniveduua-article-961 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:43:42Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | 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 |
| spellingShingle | \(n\)-real \(n\)-real closed 12D15 Feigelstock, Shalom \(N\) – real fields |
| title | \(N\) – real fields |
| title_full | \(N\) – real fields |
| title_fullStr | \(N\) – real fields |
| title_full_unstemmed | \(N\) – real fields |
| title_short | \(N\) – real fields |
| title_sort | \(n\) – real fields |
| topic | \(n\)-real \(n\)-real closed 12D15 |
| topic_facet | \(n\)-real \(n\)-real closed 12D15 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/961 |
| work_keys_str_mv | AT feigelstockshalom nrealfields |