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Fundam. Prikl. Mat., 2012, Volume 17, Issue 8, Pages 63–76 (Mi fpm1472)  

This article is cited in 1 scientific paper (total in 1 paper)

Absolute nil-ideals of Abelian groups

E. I. Kompantseva

Moscow State Pedagogical University

Abstract: It is known that in an Abelian group $G$ that contains no nonzero divisible torsion-free subgroups the intersection of upper nil-radicals of all the rings on $G$ is $\bigcap_ppT(G)$, where $T(G)$ is the torsion part of $G$. In this work, we define a pure fully invariant subgroup $G^*\supseteq T(G)$ of an arbitrary Abelian mixed group $G$ and prove that if $G$ contains no nonzero torsion-free subgroups, then the subgroup $\bigcap_ppG^*$ is a nil-ideal in any ring on $G$, and the first Ulm subgroup $G^1$ is its nilpotent ideal.

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English version:
Journal of Mathematical Sciences (New York), 2014, 197:5, 625–634

UDC: 512.541
BBK: 0https://edit.mathnet.ru/gifs/star.gif

Citation: E. I. Kompantseva, “Absolute nil-ideals of Abelian groups”, Fundam. Prikl. Mat., 17:8 (2012), 63–76; J. Math. Sci., 197:5 (2014), 625–634

Citation in format AMSBIB
\Bibitem{Kom12}
\by E.~I.~Kompantseva
\paper Absolute nil-ideals of Abelian groups
\jour Fundam. Prikl. Mat.
\yr 2012
\vol 17
\issue 8
\pages 63--76
\mathnet{http://mi.mathnet.ru/fpm1472}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 197
\issue 5
\pages 625--634
\crossref{https://doi.org/10.1007/s10958-014-1745-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84893871324}


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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. E. I. Kompantseva, “Abelian dqt-groups and rings on them”, J. Math. Sci., 206:5 (2015), 494–504  mathnet  crossref  mathscinet
  • Фундаментальная и прикладная математика
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