\(N\) – 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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Бібліографічні деталі
Дата:2018
Автор: Feigelstock, Shalom
Формат: Стаття
Мова:English
Опубліковано: Lugansk National Taras Shevchenko University 2018
Теми:
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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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-961
record_format ojs
spelling 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
institution Algebra and Discrete Mathematics
collection OJS
language English
topic \(n\)-real
\(n\)-real closed
12D15
spellingShingle \(n\)-real
\(n\)-real closed
12D15
Feigelstock, Shalom
\(N\) – real fields
topic_facet \(n\)-real
\(n\)-real closed
12D15
format Article
author Feigelstock, Shalom
author_facet Feigelstock, Shalom
author_sort Feigelstock, Shalom
title \(N\) – real fields
title_short \(N\) – 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
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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