N – real fields

Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/64

Title:	N – real fields
Authors:	Feigelstock, Shalom
Issue Date:	3-Mar-2003
Publisher:	Луганский национальный университет им. Т. Шевченко
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
URI:	http://hdl.handle.net/123456789/64
Appears in Collections:	Статті

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