On the Bassian property for Abelian groups

Authors

Andrey R. Chekhlov, Tomsk State University
Peter V. Danchev, Bulgarian Academy of Sciences
Brendan Goldsmith, Technological University DublinFollow

Document Type

Article

Rights

Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence

Disciplines

1.1 MATHEMATICS

Publication Details

Archiv der Mathematik (Basel)

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.

DOI

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

Recommended Citation

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