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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.
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
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