Quasi-Complete Primary Components in Modular Abelian Group Rings over Special Rings

Abstract

 Let \(G\) be a multiplicatively written \(p\)-separable abelian group and \(R\) a commutative unitary ring of prime characteristic \(p\) so that \(R_p^i\) has nilpotent elements for each positive integer \(i \geq 1.\) Then, we prove that, the normed unit \(p\)-subgroup \(S(RG)\) of the group ring \(RG\) is quasi-complete if and only if \(G\) is a bounded p-group. This strengthens our recent results in (Internat. J. Math. Analysis, 2006) and (Scientia Ser. A - Math., 2006).