\(N\) – 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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Дата: | 2018 |
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Lugansk National Taras Shevchenko University
2018
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Онлайн доступ: | 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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oai:ojs.admjournal.luguniv.edu.ua: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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English |
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\(n\)-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 |
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Article |
author |
Feigelstock, Shalom |
author_facet |
Feigelstock, Shalom |
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Feigelstock, Shalom |
title |
\(N\) – real fields |
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\(N\) – real fields |
title_full |
\(N\) – real fields |
title_fullStr |
\(N\) – real fields |
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\(N\) – 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 |
work_keys_str_mv |
AT feigelstockshalom nrealfields |
first_indexed |
2024-04-12T06:25:30Z |
last_indexed |
2024-04-12T06:25:30Z |
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