On the Bassian property for Abelian groups

Andrey R. Chekhlov; Peter V. Danchev; Brendan Goldsmith

doi:10.1007/s00013-021-01655-4

On the Bassian property for Abelian groups

Andrey R. Chekhlov
, Peter V. Danchev
, Brendan Goldsmith

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	593-600
Number of pages	8
Journal	Archiv der Mathematik
Volume	117
Issue number	6
DOIs	https://doi.org/10.1007/s00013-021-01655-4
Publication status	Published - Dec 2021
Externally published	Yes

Keywords

Abelian group
Bassian group
Hopfian group
Rank

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10.1007/s00013-021-01655-4Licence: Unspecified

https://arrow.tudublin.ie/scschmatart/334Licence: CC BY-NC-SA

Cite this

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title = "On the Bassian property for Abelian groups",

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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AU - Chekhlov, Andrey R.

AU - Danchev, Peter V.

AU - Goldsmith, Brendan

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AB - 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.

KW - Abelian group

KW - Bassian group

KW - Hopfian group

KW - Rank

UR - https://www.scopus.com/pages/publications/85114443160

U2 - 10.1007/s00013-021-01655-4

DO - 10.1007/s00013-021-01655-4

M3 - Article

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VL - 117

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EP - 600

JO - Archiv der Mathematik

JF - Archiv der Mathematik

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ER -

On the Bassian property for Abelian groups

Abstract

Keywords

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