Kozioł, Krzysztof Quadratic form schemes determined by Hermitian forms. (English) Zbl 0621.10016 Colloq. Math. 53, No. 1-2, 27-33 (1987). A quadratic form scheme is a triple \(S=(g,-1,d)\) where g is an elementary 2-group, -1 is in g, \(d: g\to \{subgroups\) of \(g\}\) and certain axioms hold. These axioms imitate the behavior of quadratic forms over a field F of characteristic \(\neq 2\), using \(g=F^{\times}/F^{\times 2}\), \(-1=(- 1)F^{\times 2}\), and \(d(a)=D_ F(<1,a>)/F^{\times 2}\) (the set of square classes represented by the binary quadratic form \(<1,a>)\). It is unknown whether every scheme S does arise this way from a field. The author shows that Hermitian forms over a division ring with involution also provide examples of a quadratic form scheme. Reviewer: D.B.Shapiro MSC: 11E16 General binary quadratic forms Keywords:quadratic form scheme; Hermitian forms; division ring with involution PDFBibTeX XMLCite \textit{K. Kozioł}, Colloq. Math. 53, No. 1--2, 27--33 (1987; Zbl 0621.10016) Full Text: DOI