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p-Adic representations of rings with power basis

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Abstract

Let Λ=C[x]/(r1(x)...rs(x)). Yakovlev [1] constructed a category whose indecomposable objects are in one-to-one correspondence with the indecomposable Λ-modules that are free and finitely generated over C. However, this was done for the case when all the ideals of the ring Ci=C[x]/(ri(x)) are principal. In the present article the case when Ci 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 Zp[√p] and the cyclic group of third order over Z3[3√3].

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Literature cited

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Authors and Affiliations

  1. Leningrad Scientific-Research Institute of Sea Transport, USSR

    N. M. Kopelevich

Authors
  1. N. M. Kopelevich
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Additional information

Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 265–276, February, 1975.

The author thanks A. V. Yakovlev for stating the problem and for his attention to my work.

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Kopelevich, N.M. p-Adic representations of rings with power basis. Mathematical Notes of the Academy of Sciences of the USSR 17, 154–160 (1975). https://doi.org/10.1007/BF01161872

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  • DOI: https://doi.org/10.1007/BF01161872

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