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On the Bassian property for Abelian groups

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Abstract

We define an object (group, ring, module, algebra, etc.) to be Bassian if it is not possible to embed it in a proper homomorphic image of itself. Here we study this concept for Abelian groups and achieve a complete characterization of all such groups in terms of their associated torsion-free and p-primary ranks.

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Acknowledgements

The authors would like to thank the anonymous referee and the handling editor for their careful reading of the manuscript.

Funding

The second named author (P.V. Danchev) was supported in part by the Bulgarian National Science Fund under Grant KP-06 No. 32/1 of December 07, 2019.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Tomsk State University, 634050, Tomsk, Russia

    Andrey R. Chekhlov

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Peter V. Danchev

  3. Technological University Dublin, City Campus, Lowe Grangegorman Dublin 7, Ireland

    Brendan Goldsmith

Authors
  1. Andrey R. Chekhlov
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  2. Peter V. Danchev
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  3. Brendan Goldsmith
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Correspondence to Peter V. Danchev.

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Chekhlov, A.R., Danchev, P.V. & Goldsmith, B. On the Bassian property for Abelian groups. Arch. Math. 117, 593–600 (2021). https://doi.org/10.1007/s00013-021-01655-4

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  • DOI: https://doi.org/10.1007/s00013-021-01655-4

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