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

In Memory of Rüdiger Göbel

  • Book
  • © 2017

Overview

Editors:
  1. Manfred Droste

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

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  2. László Fuchs

    1. Department of Mathematics, Tulane University, New Orleans, USA

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  3. Brendan Goldsmith

    1. Dublin Institute of Technology, Dublin, Ireland

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  4. Lutz Strüngmann

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

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  • Provides new and striking material in group theory and model theory

  • Presents a balanced mix of survey papers that will appeal to a wide audience ranging from beginning graduate students to experienced researchers

  • Includes research papers that reflect the most current research in the field

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Table of contents (28 chapters)

  1. Front Matter

    Pages i-xxxiv
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  2. Survey Articles

    1. Front Matter

      Pages 1-1
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    2. Properties of Abelian Groups Determined by Their Endomorphism Ring

      • Ulrich Albrecht
      Pages 3-22

    3. The Zero-Divisor Graph of a Commutative Semigroup: A Survey

      • David F. Anderson, Ayman Badawi
      Pages 23-39

    4. A Remak-Krull-Schmidt Class of Torsion-Free Abelian Groups

      • David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak
      Pages 41-68

    5. Rigid ℵ1-Free Abelian Groups with Prescribed Factors and Their Role in the Theory of Cellular Covers

      • Gábor Braun, Lutz Strüngmann
      Pages 69-81

    6. Definable Valuations Induced by Definable Subgroups

      • Katharina Dupont
      Pages 83-108

    7. Groups of Automorphisms of Totally Ordered Sets: Techniques, Model Theory and Applications to Decision Problems

      • A. M. W. Glass
      Pages 109-134

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

      • Brendan Goldsmith, Luigi Salce
      Pages 135-174

    9. On Subsets and Subgroups Defined by Commutators and Some Related Questions

      • Luise-Charlotte Kappe, Patrizia Longobardi, Mercede Maj
      Pages 175-189

    10. Recent Progress in Module Approximations

      • Jan Trlifaj
      Pages 191-209

  3. Research Articles

    1. Front Matter

      Pages 211-211
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    2. A Class of Pure Subgroups of the Specker Group

      • A. L. S. Corner
      Pages 213-223

    3. Countable 1-Transitive Trees

      • Katie M. Chicot, John K. Truss
      Pages 225-268

    4. On Ore’s Theorem and Universal Words for Permutations and Injections of Infinite Sets

      • Manfred Droste
      Pages 269-275

    5. An Extension of M. C. R. Butler’s Theorem on Endomorphism Rings

      • Manfred Dugas, Daniel Herden, Saharon Shelah
      Pages 277-284

    6. The Jacobson Radical’s Role in Isomorphism Theorems for p-Adic Modules Extends to Topological Isomorphism

      • Mary Flagg
      Pages 285-300

    7. A Note on Hieronymi’s Theorem: Every Definably Complete Structure Is Definably Baire

      • Antongiulio Fornasiero
      Pages 301-315

    8. Cotorsion and Tor Pairs and Finitistic Dimensions over Commutative Rings

      • László Fuchs
      Pages 317-330

    9. Permutation Groups Without Irreducible Elements

      • A. M. W. Glass, H. Dugald Macpherson
      Pages 331-332
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Keywords

About this book

This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas.  With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations.
 
The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory. 


Editors and Affiliations

  • Institut für Informatik, Universität Leipzig, Leipzig, Germany

    Manfred Droste

  • Department of Mathematics, Tulane University, New Orleans, USA

    László Fuchs

  • Dublin Institute of Technology, Dublin, Ireland

    Brendan Goldsmith

  • Faculty for Computer Sciences, Mannheim University of Applied Sciences, Mannheim, Germany

    Lutz Strüngmann

About the editors

Manfred Droste is Professor and Head of the Automata and Formal Languages Research Group in the Department of Computer Science at the University of Leipzig. His research interests include such theoretical computer science topics as automata theory, logic, algebraic models for concurrent systems, and domain theory, and such mathematical topics as model theory, automorphism groups, and ordered algebraic structures. He is editor of the Handbook of Weighted Automata.


László Fuchs is the Evelyn and John G. Phillips Distinguished Professor Emeritus in Mathematics at Tulane University. He was awarded the Kossuth Prize in 1953 and is a foreign member of the Hungarian Academy of Sciences. His research interests include abelian groups, commutative domains and their modules. He is the author of numerous publications, including Abelian Groups (Springer Monographs in Mathematics). 


Brendan Goldsmith is Research Director at the School of Mathematical Sciences of the Dublin Institute of Technology. Formerly, he served as Head of the School of Mathematics and President of DIT. His research interests include group theory and generalizations, commutative algebra, associative rings and algebras, and mathematical logic.


Lutz Strüngmann is Professor of Mathematics at the University of Duisberg-Essen. He has authored 56 publications since 1999 in the fields of group theory and generalizations, mathematical logic, commutative algebra and associative rings and algebras.

Bibliographic Information

  • Book Title: Groups, Modules, and Model Theory - Surveys and Recent Developments

  • Book Subtitle: In Memory of Rüdiger Göbel

  • Editors: Manfred Droste, László Fuchs, Brendan Goldsmith, Lutz Strüngmann

  • DOI: https://doi.org/10.1007/978-3-319-51718-6

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • License: CC BY

  • Hardcover ISBN: 978-3-319-51717-9Published: 12 June 2017

  • Softcover ISBN: 978-3-319-84725-2Published: 01 August 2018

  • eBook ISBN: 978-3-319-51718-6Published: 02 June 2017

  • Edition Number: 1

  • Number of Pages: XXXIV, 475

  • Number of Illustrations: 30 b/w illustrations

  • Topics: Group Theory and Generalizations

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