COMMUTATIVE GROUP ALGEBRAS OF p^{ω +n} - PROJECTIVE ABELIAN GROUPS

Peter Danchev

Abstract

          Suppose G is an abelian group and R is a unitary commutative ring of prime characteristic p. The first main result is that the p^{ω +1}-projective p-group G is a direct factor of the group of normed units V(RG) and V(RG)/G is totally projective provided R is perfect. The second main result is that the complete set of invariants for the R-algebra RG consists of G, in the cases when G is splitting or G is with torsion-free rank one and in both situations the torsion part of    is a p^{ω +1}-projective p-group. These claims strengthen a theorem due to Beers-Richman-Walker.