Abstract
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 Λ-modules that are free and finitely generated over Λ and different from certain completely defined Λ-modules with one generator. With the help of our result, we describe the indecomposable p-adic representations of the ring Λ=Zp [x]/((1−x)2 (1 + x +...+ x)p−1).
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A. V. Yakovlev, “Homological determinacy of the p-adic representations of rings with power basis,” Izv. Akad. Nauk SSSR, Ser. Matem.,34, No 5, 1000–1014 (1970).
N. Bourbaki, Algebra [Russian translation], Moscow (1966).
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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.
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Kopelevich, N.M. Homological determinacy of the p-adic representations of nonsemisimple rings with power basis. Mathematical Notes of the Academy of Sciences of the USSR 14, 793–798 (1973). https://doi.org/10.1007/BF01147458
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DOI: https://doi.org/10.1007/BF01147458