On the Bassian property for Abelian groups

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 -...

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Bibliographic Details
Published inArchiv der Mathematik Vol. 117; no. 6; pp. 593 - 600
Main Authors Chekhlov, Andrey R., Danchev, Peter V., Goldsmith, Brendan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2021
Springer Nature B.V
Subjects
Group theory
Mathematics
Mathematics and Statistics
Rings (mathematics)
Abelian group
Hopfian group
Bassian group
Rank
20K10
20K21
20K20
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Summary: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.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-021-01655-4