Invariants of group rings (Q1115939)

The invariants of group rings RG that are discussed here are the Schur index \(M_{\chi}(R)\), the Schur exponent \(m_{\chi}(R)\), the Schur group S(R), and the uniform group U(R). The ring R is supposed to be commutative and to contain the group order in its unit group; \(\chi\) is a character of G belonging to a finitely generated projective RG-module. The definitions of the objects mentioned above already stem from earlier papers by Szeto, Mollin, de Meyer \& Mollin, and Greenfield \& Mollin. We'd like to mention some of the results: \(m_{\chi}(R)| M_{\chi}(R)\) (possibly equality holds); S(R)\(\subset U(R)\subset B(R)\), B(R) being the Brauer group of R; for each \(n\in N\) there is a local field K such that U(K)/S(K) is cyclic of order n. For a perfect field k, \(U(k[t,t^{-1}])\) is determined.