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Properties of Abelian Groups Determined by Their Endomorphism Ring

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Groups, Modules, and Model Theory - Surveys and Recent Developments

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Abstract

The goal of this paper is to give a survey of how endomorphism rings can be used to study the behavior of modules. While the first part considers modules over arbitrary rings, the second half focuses mainly on the case of torsion-free Abelian groups. Although there are many applications of endomorphism rings to the theory of mixed Abelian groups, a comprehensive discussion of this subject is beyond the framework of a survey article. In particular, we only present core results, and provide an extensive literature list for those who want to get deeper into the subject.

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Acknowledgements

I had known Rüdiger since 1976 when I took Linear Algebra from him as a freshman. I want to use this opportunity to express my appreciation for his support and friendship during almost 40 years.

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Authors and Affiliations

  1. Department of Mathematics, Auburn University, Auburn, AL, 36849, USA

    Ulrich Albrecht

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  1. Ulrich Albrecht
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Correspondence to Ulrich Albrecht .

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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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Albrecht, U. (2017). Properties of Abelian Groups Determined by Their Endomorphism Ring. 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_1

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