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

Part I. Survey Articles

1. Properties of Abelian Groups Determined by Their Endomorphism Ring
Ulrich Albrecht

2. The Zero-Divisor Graph of a Commutative Semigroup: A Survey
David F. Anderson, Ayman Badawi

3. A Remak-Krull-Schmidt Class of Torsion-Free Abelian Groups
David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak

4. Rigid ℵ1-Free Abelian Groups with Prescribed Factors and Their Role in the Theory of Cellular Covers
Gábor Braun, Lutz Strüngmann

5. Definable Valuations Induced by Definable Subgroups
Katharina Dupont

6. Groups of Automorphisms of Totally Ordered Sets: Techniques, Model Theory and Applications to Decision Problems
A. M. W. Glass

7. Algebraic Entropies for Abelian Groups with Applications to the Structure of Their Endomorphism Rings: A Survey
Brendan Goldsmith, Luigi Salce

8. On Subsets and Subgroups Defined by Commutators and Some Related Questions
Luise-Charlotte Kappe, Patrizia Longobardi, Mercede Maj

9. Recent Progress in Module Approximations
Jan Trlifaj

Part II. Research Articles

10. A Class of Pure Subgroups of the Specker Group
A. L. S. Corner

11. Countable 1-Transitive Trees
Katie M. Chicot, John K. Truss

12. On Ore’s Theorem and Universal Words for Permutations and Injections of Infinite Sets
Manfred Droste

13. An Extension of M. C. R. Butler’s Theorem on Endomorphism Rings
Manfred Dugas, Daniel Herden, Saharon Shelah

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

15. A Note on Hieronymi’s Theorem: Every Definably Complete Structure Is Definably Baire
Antongiulio Fornasiero

16. Cotorsion and Tor Pairs and Finitistic Dimensions over Commutative Rings
László Fuchs

17. Permutation Groups Without Irreducible Elements
A. M. W. Glass, H. Dugald Macpherson

18. R-Hopfian and L-co-Hopfian Abelian Groups (with an Appendix by A.L.S. Corner on Near Automorphisms of an Abelian Group)
Brendan Goldsmith, Ketao Gong

19. On the Abelianization of Certain Topologist’s Products
Wolfgang Herfort, Wolfram Hojka

20. Some Remarks on dp-Minimal Groups
Itay Kaplan, Elad Levi, Pierre Simon

21. Square Subgroups of Decomposable Rank Three Groups
Fatemeh Karimi

22. An Invariant on Primary Abelian Groups with Applications to Their Projective Dimensions
Patrick W. Keef

23. The Valuation Difference Rank of a Quasi-Ordered Difference Field
Salma Kuhlmann, Mickaël Matusinski, Françoise Point

24. The Lattice of U-Sequences of an Abelian p-Group
K. Robin McLean

25. Strongly Non-Singular Rings and Morita Equivalence
Bradley McQuaig

26. The Class of (2, 3)-Groups with Homocyclic Regulator Quotient of Exponent p
2

Ebru Solak

27. Unbounded Monotone Subgroups of the Baer–Specker Group
Burkhard Wald

28. Clusterization of Correlation Functions
Alexander Zuevsky

Avainsanat: Mathematics, Group Theory and Generalizations