Homological determinacy of the $p$-adic representations of nonsemisimple rings with power basis

A result on the homological determinacy of the $p$-adic representations of semisimple rings with power basis is extended to nonsemisimple rings. We construct a category whose in-decomposable objects are in one-to-one correspondence with indecomposable $\Lambda$-modules that are free and finitely generated over $\Lambda$ and different from certain completely defined $\Lambda$-modules with one generator. With the help of our result, we describe the indecomposable p-adic representations of the ring $\Lambda=Z_p[x]/((1-x)^2(1+x+\dots+x)^{p-1})$.