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 -modules that are free and finitely generated over and different from certain completely defined -modules with one generator. With the help of our result, we describe the indecomposable p-adic representations of the ring =Zp x]/((1–x)² (1 + x +...+ x)^p–1).Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 407–417, September, 1973.The author thanks A. V. Yakovlev for stating the problem and for his valuable observations.