N – real fields

dc.contributor.author	Feigelstock, S.
dc.date.accessioned	2019-06-17T10:42:57Z
dc.date.available	2019-06-17T10:42:57Z
dc.date.issued	2003
dc.identifier.citation	N – real fields / S. Feigelstock // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 3. — С. 1–6. — Бібліогр.: 8 назв. — англ.	uk_UA
dc.identifier.issn	1726-3255
dc.identifier.other	2000 Mathematics Subject Classification: 12D15.
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/155693
dc.description.abstract	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	Інститут прикладної математики і механіки НАН України	uk_UA
dc.relation.ispartof	Algebra and Discrete Mathematics
dc.title	N – real fields	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA