Integral Representations of Cyclic Groups of Orderp2

Letpbe any prime number,Gbe the cyclic group of orderp2, and Λ RGbe the group algebra ofGover a Dedekind domainRsuch thatpRis a maximal ideal inRand bothR[T]/Φp(T) andR[T]/Φp2(T) are Dedekind domains also, where Φn(T) is thenth cyclotomic polynomial. We shall provide a full list of indecomposable Λ lattices constructed in an explicit way. A complete set of invariants of these indecomposable Λ lattices will be determined also, under an additional assumption onR. The above results were obtained by Reiner [Pacific J. Math.78(1978), 467–501] whenR = Z.