Let G be an finite group. Consider the group ring C[G] := {ΣgeGagg: ag € C}. The addition is given by (ΣgeG ª99) + (ΣgeGbgg) := ΣgeG (ag+bg)g and the multiplica- tion is given by Show that N := (Σagg) (Σbnh) := ΣΙΣ agn-1bn)g. gEG heG gEG heG ΣgeGagg € C[G] : ΣgeG ag = 0} is an ideal of C[G]. What is C[G]/N?

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