Idempotents in \(F_+(G)\)

In this paper, we compute the idempotents of the ring \(F_+(G)\) as defined by Boltje (J Algebra 206:293–343, 1998) in the particular case when the Green biset functor F is such that for all subgroups H of a finite group G, F(H) is a torsion-free ring, finitely-generated as an Abelian group, and has only the trivial idempotents. In this case, the only idempotents in \(F_+(G)\) are those arising from the Burnside ring B(G).