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The Krull―Schmidt Theorem for Henselian Rings

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Abstract

A necessary and sufficient condition on a local ring over which all indecomposable finite-dimensional algebras are local is found. The Krull―Schmidt theorem for a class of rings that includes both the Henselian valuation rings and the rings of integers of multidimensional fields is proved. Bibliography: 2 titles.

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REFERENCES

  1. Z. I. Borevich and D. K. Faddeev, “Homology theory in groups. II. Projective resolvents of finite groups,” Vestn. Leningr. Univ., 7, 72–81 (1959).

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  2. J.-P. Serre, Local Fields, Graduate Texts in Mathematics, 67, Springer-Verlag, Berlin-Heidelberg-New York (1979).

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Authors and Affiliations

  1. St.Petersburg State University, Russia

    M. V. Bondarko

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  1. M. V. Bondarko
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Bondarko, M.V. The Krull―Schmidt Theorem for Henselian Rings. Journal of Mathematical Sciences 112, 4259–4265 (2002). https://doi.org/10.1023/A:1020326532006

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  • DOI: https://doi.org/10.1023/A:1020326532006

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