THE PERIODIC RADICAL OF GROUP RINGS AND INCIDENCE ALGEBRAS

Let R be a ring with 1 and P(R) the periodic radical of R. We obtain necessary and sufficient conditions forP(RG) = 0 when RG is the group ring of an FC group G and R is commutative. We also obtain a complete description of P I(X R) when I(X R) is the incidence algebra of a locally finite partially ordered set X and R is commutative.