\(N\) – real fields

• Date: 2018
• Main Author: Feigelstock, Shalom
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: \(n\)-real; \(n\)-real closed; 12D15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/961
• Journal Title: Algebra and Discrete Mathematics

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...