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Fundam. Prikl. Mat., 2010, Volume 16, Issue 7, Pages 221–236 (Mi fpm1372)  

This article is cited in 7 scientific papers (total in 7 papers)

$E$-solvable modules

A. R. Chekhlov

Tomsk State University

Abstract: $E$-nilpotent and $E$-solvable modules have been defined. Some properties of such modules have been proved. For instance, all direct summands of an $E$-nilpotent module are fully invariant, and the $E$-commutant of an $E$-solvable module is contained in the intersection of all maximal commutatorically invariant submodules. Necessary and sufficient conditions under which a finite length module is $E$-solvable have been found.

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English version:
Journal of Mathematical Sciences (New York), 2012, 183:3, 424–434

Bibliographic databases:

UDC: 512.553

Citation: A. R. Chekhlov, “$E$-solvable modules”, Fundam. Prikl. Mat., 16:7 (2010), 221–236; J. Math. Sci., 183:3 (2012), 424–434

Citation in format AMSBIB
\Bibitem{Che10}
\by A.~R.~Chekhlov
\paper $E$-solvable modules
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 7
\pages 221--236
\mathnet{http://mi.mathnet.ru/fpm1372}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2846230}
\transl
\jour J. Math. Sci.
\yr 2012
\vol 183
\issue 3
\pages 424--434
\crossref{https://doi.org/10.1007/s10958-012-0823-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84861454074}


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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. R. Chekhlov, “E-engelevy abelevy gruppy stupeni $\le2$”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2012, no. 1(17), 54–60  mathnet
    2. A. R. Chekhlov, “Abelian groups with nilpotent commutators of endomorphisms”, Russian Math. (Iz. VUZ), 56:10 (2012), 50–61  mathnet  crossref  mathscinet
    3. A. R. Chekhlov, “On Abelian groups close to $E$-solvable groups”, J. Math. Sci., 197:5 (2014), 708–733  mathnet  crossref
    4. A. R. Chekhlov, Ml. V. Agafontseva, “Ob abelevykh gruppakh s tsentralnymi kvadratami kommutatorov endomorfizmov”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2013, no. 4(24), 54–59  mathnet  elib
    5. A. R. Chekhlov, “On abelian groups with right-invariant isometries”, Siberian Math. J., 55:3 (2014), 574–577  mathnet  crossref  mathscinet  isi  elib  elib
    6. Chekhlov A.R. Danchev P.V., “on Commutator Fully Transitive Abelian Groups”, J. Group Theory, 18:4 (2015), 623–647  crossref  mathscinet  zmath  isi  elib
    7. A. R. Chekhlov, “On Abelian groups with commutative commutators of endomorphisms”, J. Math. Sci., 230:3 (2018), 502–506  mathnet  crossref  mathscinet  elib
  • Фундаментальная и прикладная математика
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