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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 4, Pages 715–736 (Mi izv2318)  

This article is cited in 4 scientific papers (total in 4 papers)

Primary orders with a finite numbers of indecomposable representations

Yu. A. Drozd, V. V. Kirichenko


Abstract: Let $\Lambda$ be a semisimple $Z$-ring and $C$ its center. Assume that for any prime ideal $\mathfrak p\subset C$ the ring $\Lambda_{\mathfrak p}$ is primary. Let $\overline\Lambda$ be the intersection of the maximal over-rings of $\Lambda$, $I=\overline\Lambda/\Lambda$ and $I'=\operatorname{rad}I$. We prove that $\Lambda$ has a finite number of indecomposable integral representations if and only if $\overline\Lambda$ is a hereditary ring, $I$ has two generators as a $\Lambda$-module, and $I'$ is cyclic.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:4, 711–732

Bibliographic databases:

UDC: 519.49
MSC: Primary 16A18, 16A64; Secondary 16A40
Received: 14.03.1972

Citation: Yu. A. Drozd, V. V. Kirichenko, “Primary orders with a finite numbers of indecomposable representations”, Izv. Akad. Nauk SSSR Ser. Mat., 37:4 (1973), 715–736; Math. USSR-Izv., 7:4 (1973), 711–732

Citation in format AMSBIB
\Bibitem{DroKir73}
\by Yu.~A.~Drozd, V.~V.~Kirichenko
\paper Primary orders with a~finite numbers of indecomposable representations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 4
\pages 715--736
\mathnet{http://mi.mathnet.ru/izv2318}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=325694}
\zmath{https://zbmath.org/?q=an:0291.16005}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 4
\pages 711--732
\crossref{https://doi.org/10.1070/IM1973v007n04ABEH001973}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. F. Barannik, P. M. Gudivok, “Crossed group rings of finite groups and rings of $p$-adic integers with finitely many indecomposable integral representations”, Math. USSR-Sb., 36:2 (1980), 173–194  mathnet  crossref  mathscinet  zmath  isi
    2. Jeremy Haefner, “On Gorenstein orders”, Journal of Algebra, 132:2 (1990), 406  crossref
    3. Jeremy Haefner, “On local orders”, Journal of Algebra, 139:1 (1991), 195  crossref
    4. Hiroaki Hijikata, Kenji Nishida, “Primary Orders of Finite Representation Type”, Journal of Algebra, 192:2 (1997), 592  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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