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 (AAt
 ) = 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...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2003 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2003
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155693 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | N – real fields / S. Feigelstock // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 3. — С. 1–6. — Бібліогр.: 8 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 (AAt
) = 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.
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| ISSN: | 1726-3255 |