The group algebra

  • Jean-Pierre Serre
Part of the Graduate Texts in Mathematics book series (GTM, volume 42)


Let G be a group of finite order g, and let K be a commutative ring. We denote by K[G] the algebra of G over K; this algebra has a basis indexed by the elements of G, and most of the time we identify this basis with G. Each element f of K[G] can then be uniquely written in the form
$$ f = \sum\limits_{s \in G} {{a_s}} s,with{a_s} \in K, $$
and multiplication in K[G] extends that in G.


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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Chaire d’algèbre et géométrieCollège de FranceParisFrance

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