$p$-Adic representations of rings with power basis

Let $\Lambda=C[x]/(r_1(x)\dots r_3(x))$. Yakovlev [1] constructed a category whose indecomposable objects are in one-to-one correspondence with the indecomposable $\Lambda$-modules that are free and finitely generated over $C$. However, this was done for the case when all the ideals of the ring $C_i=C[x]/(r_i(x))$ are principal. In the present article the case when $C_i$ has ideals with two generators is investigated. With the help of the results obtained a description is given of the integral representations of the cyclic group of $p$-th order over $Z_p[\sqrt p]$ and the cyclic group of third order over $Z_3[\sqrt[3]3]$.