2010/04/14 by Detlev W. Hoffmann, Hoffmann, Detlev W.
Computer Science · Mathematics · #11E04 #11E10 #11E81 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #math.RA #msc:11E04 #msc:11E10 #msc:11E81
paper · pdf · doi:10.48550/arxiv.1004.2483
11 pages
arxiv created 2010/04/14 · openalex publication_date 2010/04/14 · arxiv updated 2010/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let F be a field of characteristic different from 2. The u-invariant and the Hasse number of a field F are classical and important field invariants pertaining to quadratic forms. These invariants measure the suprema of dimensions of anisotropic forms over F that satisfy certain additional properties. We construct various examples of fields with infinite Hasse number and prescribed finite values of u that satisfy additional properties pertaining to the space of orderings of the field. We also construct to each positive integer n a real field F such such that the Hasse number is 2n+1 and such that each quadratic form over F of dimension 1+2n is a Pfister neighbor. These results were announced (without proof) in the article "Dimensions of anisotropic indefinite quadratic forms II" by the present author.