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 |
|---|---|
| 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| _version_ | 1862533437400809472 |
|---|---|
| author | Feigelstock, S. |
| author_facet | Feigelstock, S. |
| citation_txt | N – real fields / S. Feigelstock // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 3. — С. 1–6. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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 (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.
|
| first_indexed | 2025-11-24T06:35:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155693 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-24T06:35:03Z |
| publishDate | 2003 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Feigelstock, S. 2019-06-17T10:42:57Z 2019-06-17T10:42:57Z 2003 N – real fields / S. Feigelstock // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 3. — С. 1–6. — Бібліогр.: 8 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 12D15. https://nasplib.isofts.kiev.ua/handle/123456789/155693 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics N – real fields Article published earlier |
| spellingShingle | N – real fields Feigelstock, S. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155693 |
| work_keys_str_mv | AT feigelstocks nrealfields |