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Fundam. Prikl. Mat., 2009, Volume 15, Issue 8, Pages 95–143 (Mi fpm1283)  

This article is cited in 5 scientific papers (total in 5 papers)

Torsion-free rings

E. I. Kompantseva

Moscow State Pedagogical University

Abstract: The aim of this paper is to study the correlation between the properties of rings and the structure of their additive groups. In this paper, all multiplications on reduced algebraically compact groups and on divisible torsion-free Abelian groups are described. Absolute Jacobson radicals and absolute nil-radicals in some classes of Abelian groups are found. Using these results, we will give a description of semisimple groups and also of groups on which every ring is a nilpotent ring (a nil-ring, a radical ring) in some concerned classes of Abelian groups.

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English version:
Journal of Mathematical Sciences (New York), 2010, 171:2, 213–247

Bibliographic databases:

UDC: 512.541

Citation: E. I. Kompantseva, “Torsion-free rings”, Fundam. Prikl. Mat., 15:8 (2009), 95–143; J. Math. Sci., 171:2 (2010), 213–247

Citation in format AMSBIB
\Bibitem{Kom09}
\by E.~I.~Kompantseva
\paper Torsion-free rings
\jour Fundam. Prikl. Mat.
\yr 2009
\vol 15
\issue 8
\pages 95--143
\mathnet{http://mi.mathnet.ru/fpm1283}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2745015}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 171
\issue 2
\pages 213--247
\crossref{https://doi.org/10.1007/s10958-010-0132-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78149496812}


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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. E. I. Kompantseva, “Absolute nil-ideals of Abelian groups”, J. Math. Sci., 197:5 (2014), 625–634  mathnet  crossref
    2. Pham Thi Thu Thuy, “Torsion Abelian RAI-groups”, J. Math. Sci., 197:5 (2014), 658–678  mathnet  crossref
    3. E. I. Kompantseva, “Abelian dqt-groups and rings on them”, J. Math. Sci., 206:5 (2015), 494–504  mathnet  crossref  mathscinet
    4. E. I. Kompantseva, Fam Tkhi Tkhu Tkhyui, “Absolyutnye idealy algebraicheski kompaktnykh abelevykh grupp”, Fundament. i prikl. matem., 22:5 (2019), 91–114  mathnet
    5. E. I. Kompantseva, “Koltsa na vektornykh abelevykh gruppakh”, Fundament. i prikl. matem., 22:5 (2019), 243–258  mathnet
  • Фундаментальная и прикладная математика
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