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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 F is not n-real. It is shown that if a 3...
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Інститут прикладної математики і механіки НАН України
2003
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/155693 |
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irk-123456789-1556932019-06-18T01:26:11Z N – real fields Feigelstock, S. 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. 2003 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/155693 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Feigelstock, S. |
| spellingShingle |
Feigelstock, S. N – real fields Algebra and Discrete Mathematics |
| author_facet |
Feigelstock, S. |
| author_sort |
Feigelstock, S. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2003 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155693 |
| citation_txt |
N – real fields / S. Feigelstock // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 3. — С. 1–6. — Бібліогр.: 8 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT feigelstocks nrealfields |
| first_indexed |
2023-05-20T17:46:47Z |
| last_indexed |
2023-05-20T17:46:47Z |
| _version_ |
1796154077126590464 |