Integral representations of cyclic groups of order \(p^2\) (Q1270100)

Let \(p\) be a prime number, \(G\) be the cyclic group of order \(p^2\), and \(\Lambda=RG\) be the group algebra of \(G\) over a Dedekind domain \(R\) such that \(pR\) is a maximal ideal in \(R\) and both \(R[T]/\Phi_p(T)\) and \(R[T]/\Phi_{p^2}(T)\) are Dedekind domains, where \(\Phi_n(T)\) is the \(n\)th cyclotomic polynomial. In this paper a full list of indecomposable \(\Lambda\)-lattices constructed in an explicit way is given. Invariants of these indecomposable \(\Lambda\)-lattices are determined, under an additional assumption on \(R\). \(\Lambda\)-lattices are studied via pull-back diagrams. Also necessary and sufficient conditions are determined for two indecomposable \(\Lambda\)-lattices to belong to the same genus.