Published online by Cambridge University Press: 07 September 2010
Group rings usually appear in courses on group representation theory as a means to gain a broader view of the subject and connect it to the general theory of algebras and their representations (e.g. Boerner or Curtis & Reiner). This may suggest the misleading idea that it was precisely this point of view that motivated the definition and study of group rings. In fact, this is explicitly stated by several authors who attribute the idea to E. Noether.
Though both topics are closely related and representation theory was actually a motivation for much of the work done in group rings, the historical order of development was rather the reverse: interest in the structure of group rings led to the discovery of some of the earlier theorems on group representations. This fact was pointed out in a most interesting paper by T. Hawkins but, perhaps due to the fact that it was published in a journal devoted to the history of science rather than to mathematics itself, it seems to have remained unnoticed by those working on the subject. Recent books and surveys fail to credit either A. Cayley or T. Molien, and some still attribute to E. Noether the creation of the theory, omitting even the influence of R. Brauer.