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Originally published in 1983, the principal object of this book is to discuss in detail the structure of finite group rings over fields of characteristic, p, P-adic rings and, in some cases, just principal ideal domains, as well as modules of such group rings. The approach does not emphasize any particular point of view, but aims to present a smooth proof in each case to provide the reader with maximum insight. However, the trace map and all its properties have been used extensively. This generalizes a number of classical results at no extra cost and also has the advantage that no assumption on the field is required. Finally, it should be mentioned that much attention is paid to the methods of homological algebra and cohomology of groups as well as connections between characteristic 0 and characteristic p.

Group algebras. --- Finite groups. --- Algebraic fields. --- Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Groups, Finite --- Group theory --- Algebras, Group --- Abelian groups --- Locally compact groups --- Algebraic fields --- Group algebras --- 512.547 --- 512.547 Linear representations of abstract groups. Group characters --- Linear representations of abstract groups. Group characters --- Modules (Algebra). --- Algèbres de groupes. --- Algèbres associatives --- Groupes finis --- Algèbres associatives --- Algèbres de groupes.