1969/08/01 by Raymond G. Ayoub, Raymond Ayoub, Christine Ayoub · 2 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.1017/s0004972700041496
The group ring of a finite abelian group G over the field of rational numbers Q and over the rational integers Z is studied. A new proof of the fact that the group ring QG is a direct sum of cyclotomic fields is given – without use of the Maschke and Wedderburn theorems; it is shown that the projections of QG onto these fields are determined by the inequivalent characters of G . It is proved that the group of units of ZG is a direct product of a finite group and a free abelian group F and the rank of F is determined. A formula for the orthogonal idempotents of QG is found.