N – real fields

dc.contributor.author	Feigelstock, Shalom
dc.date.accessioned	2015-10-20T11:54:24Z
dc.date.available	2015-10-20T11:54:24Z
dc.date.issued	2003-03-03
dc.identifier.uri	http://hdl.handle.net/123456789/64
dc.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	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Луганский национальный университет им. Т. Шевченко	uk_UA
dc.title	N – real fields	uk_UA
dc.type	Article	uk_UA