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Algebra Logika, 2004, Volume 43, Number 1, Pages 60–76 (Mi al57)  

This article is cited in 8 scientific papers (total in 8 papers)

The Jacobson Radical of an Endomorphism Ring for an Abelian Group

P. A. Krylov


Abstract: The Jacobson radical of an endomorphism ring is computed for a completely decomposable torsion-free Abelian group and for a mixed Abelian group in one class of mixed groups. For the latter case, we also look into the question when a factor ring w.r.t. the radical is regular in the sense of Nuemann.

Keywords: Abelian group, endomorphism ring, Jacobson radical.

Full text: PDF file (224 kB)
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English version:
Algebra and Logic, 2004, 43:1, 34–43

Bibliographic databases:

UDC: 512.541
Received: 04.01.2002

Citation: P. A. Krylov, “The Jacobson Radical of an Endomorphism Ring for an Abelian Group”, Algebra Logika, 43:1 (2004), 60–76; Algebra and Logic, 43:1 (2004), 34–43

Citation in format AMSBIB
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\by P.~A.~Krylov
\paper The Jacobson Radical of an Endomorphism Ring for an Abelian Group
\jour Algebra Logika
\yr 2004
\vol 43
\issue 1
\pages 60--76
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2073445}
\zmath{https://zbmath.org/?q=an:1065.20066}
\elib{https://elibrary.ru/item.asp?id=9127536}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 1
\pages 34--43
\crossref{https://doi.org/10.1023/B:ALLO.0000015129.15394.33}
\elib{https://elibrary.ru/item.asp?id=5976468}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42349091042}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Budanov, “Kvazineobratimye endomorfizmy abelevykh grupp”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2010, no. 3(11), 13–22  mathnet
    2. P. A. Krylov, A. A. Tuganbaev, “Idempotent functors and localizations in categories of modules and Abelian groups”, J. Math. Sci., 183:3 (2012), 323–382  mathnet  crossref  mathscinet
    3. K. S. Sorokin, “$SP$-gruppy s chistymi koltsami endomorfizmov”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2014, no. 4(30), 24–35  mathnet
    4. K. S. Sorokin, “$\mathrm{SP}$-gruppy ranga 2 s chistymi koltsami endomorfizmov”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2014, no. 5(31), 48–62  mathnet
    5. K. S. Sorokin, “Self-small $\mathrm{SP}$-groups with clean endomorphism rings”, J. Math. Sci., 230:3 (2018), 445–450  mathnet  crossref  mathscinet
    6. Fuchs L., “Abelian Groups”, Abelian Groups, Springer Monographs in Mathematics, Springer, 2015, 1–747  crossref  mathscinet  isi
    7. P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev, “sp-Gruppy i ikh koltsa endomorfizmov”, Algebra, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 159, VINITI RAN, M., 2019, 68–110  mathnet  mathscinet
    8. P. A. Krylov, A. A. Tuganbaev, “Moduli nad oblastyami diskretnogo normirovaniya. III”, Algebra, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 164, VINITI RAN, M., 2019, 74–95  mathnet  mathscinet
  • Алгебра и логика Algebra and Logic
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