| Summary: | In this thesis we study the group ring of an arbitrary group over an associative ring with unit element. Classically the group ring studied was that of a finite group over a field, and with the introduction of group characters a number of theorems on finite groups were derived from the theory of the group ring. (See, for example, M. Hall, The theory of groups, chapter 16). For the general group ring considered here, which allows in particular infinite groups, no such application can be claimed as yet, perhaps because the basic theory has not been sufficiently developed.
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