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Groups, Modules, and Model Theory - Surveys and Recent Developments pp 135–174Cite as

Algebraic Entropies for Abelian Groups with Applications to the Structure of Their Endomorphism Rings: A Survey

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Abstract

The algebraic entropies most frequently used for endomorphisms of Abelian groups are illustrated, their properties and mutual relationships are discussed, and several applications to endomorphism rings, both of torsion and torsion-free Abelian groups, are presented.

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Acknowledgements

The authors would like to thank the anonymous referee for the careful reading of the paper and for his/her valuable comments. The research was supported by “Progetti di Eccellenza CARIPARO 2012”.

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Authors and Affiliations

  1. Dublin Institute of Technology, The Clock Tower 032, Lower Grangegorman, Dublin 7, D07H6K8, Ireland

    Brendan Goldsmith

  2. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Luigi Salce

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  1. Brendan Goldsmith
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  2. Luigi Salce
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Correspondence to Luigi Salce .

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Editors and Affiliations

  1. Institut für Informatik, Universität Leipzig, Leipzig, Germany

    Manfred Droste

  2. Department of Mathematics, Tulane University, New Orleans, Louisiana, USA

    László Fuchs

  3. Dublin Institute of Technology, Dublin, Ireland

    Brendan Goldsmith

  4. Faculty for Computer Sciences, Mannheim University of Applied Sciences, Mannheim, Germany

    Lutz Strüngmann

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Goldsmith, B., Salce, L. (2017). Algebraic Entropies for Abelian Groups with Applications to the Structure of Their Endomorphism Rings: A Survey. In: Droste, M., Fuchs, L., Goldsmith, B., Strüngmann, L. (eds) Groups, Modules, and Model Theory - Surveys and Recent Developments . Springer, Cham. https://doi.org/10.1007/978-3-319-51718-6_7

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