Torsion-free modules over reduced Witt rings
For a ring-order \(R\), \textit{R. Wiegand} and \textit{R. Guralnick} [Lect. Notes Pure Appl. Math. 189, 333-347 (1997; Zbl 0884.13004)] defined the genus class group Genus(\(M\)) of a torsion-free, finitely generated \(R\)-module \(M\). The goal of the paper under review is to show that some of these results also hold for the reduced Witt rings of finite stability index. This generalizes previous results of the author on projective modules over Witt rings [J. Algebra 183, 286-305 (1996; Zbl 0922.11036)] to a wider class of modules. The main objects of interest are odd degree field extensions \(K\) of a formally real field \(F\) with finite stability index. The results of the paper apply to \((WK)_{\text{red}}\) considered as a \((WF)_{\text{red}}\)-module.
scientific article; zbMATH DE number 1526437
scientific article