Decomposing Witt rings of characteristic two (Q917581)

The author gives necessary and sufficient conditions for an abstract Witt ring of characteristic 2 to be a product (in the category of Witt rings) of group rings or group rings and dyadic local types. On the one hand this result has similarities with the problem of local factors discussed by \textit{R. Fitzgerald} and \textit{J. Yucas} [ibid. 16, 619--627 (1986; Zbl 0636.10018)], on the other hand it generalizes the characterization of a product of two group rings given earlier by the author and \textit{A. Carson} [Can. J. Math. 34, 1276--1302 (1982; Zbl 0516.10014)]. This result is used to get a characterization of elementary Witt rings of characteristic 2.