Witt's theorems for Galois ring valued quadratic forms (Q942204)

A Galois ring of \(q^2\) elements, where \(q=2^\ell\), is a local ring \(R\) with maximal ideal \(2R\) and residue class field \(R/2R=\text{ GF}(q)\). Quadratic forms with values in a Galois ring were studied by \textit{J. A. Wood} [Trans. Am. Math. Soc. 336, No. 1, 445--461 (1993; Zbl 0766.15033)] and the authors [Finite Fields Appl. 13, No. 4, 946--961 (2007; Zbl 1137.11024)]. Here the authors prove the Witt cancellation and the Witt extension theorems for Galois ring valued quadratic forms.