N – real fields

• Published in: Algebra and Discrete Mathematics
• Date: 2003
• Main Author: Feigelstock, S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2003
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/155693
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: N – real fields / S. Feigelstock // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 3. — С. 1–6. — Бібліогр.: 8 назв. — англ.

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...