Abelian Groups With Monomorphisms Invariant With Respect to Epimorphisms View Full Text


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Article Info

DATE

2018-12

AUTHORS

A. R. Chekhlov

ABSTRACT

If for any injective endomorphism α and surjective endomorphism β of an abelian group there exists its endomorphism γ such that βα = αγ (respectively, αβ = γα), then we say that the group possesses the R-property (respectively, the L-property). We show that if a reduced torsionfree group possesses the R-property or the L-property, then the endomorphism ring of the group is normal. We describe divisible groups and direct sums of cyclic groups possessing the R-property or the L-property. More... »

PAGES

74-80

References to SciGraph publications

  • 2014-06. Periodic groups acting freely on abelian groups in PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
  • 2018-04. On Abelian Groups with Commutative Commutators of Endomorphisms in JOURNAL OF MATHEMATICAL SCIENCES
  • 2013-09. On abelian groups with commuting monomorphisms in SIBERIAN MATHEMATICAL JOURNAL
  • 2016-09. On fully quasitransitive abelian groups in SIBERIAN MATHEMATICAL JOURNAL
  • 2014-05. On abelian groups with right-invariant isometries in SIBERIAN MATHEMATICAL JOURNAL
  • 2009-07. Abelian groups with normal endomorphism rings in ALGEBRA AND LOGIC
  • Journal

    TITLE

    Russian Mathematics

    ISSUE

    12

    VOLUME

    62

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.3103/s1066369x1812006x

    DOI

    http://dx.doi.org/10.3103/s1066369x1812006x

    DIMENSIONS

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