Abelian Group Theory and Related Topics

This volume contains the proceedings of a conference on abelian groups held in August 1993 at Oberwolfach. The conference brought together forty-seven participants from all over the world and from a range of mathematical areas. Experts from model theory, set theory, noncommutative groups, module theory, and computer science discussed problems in their fields that relate to abelian group theory. This book provides a window on the frontier of this active area of research.

Table of Contents:
Richard Scott Pierce by C. Vinsonhaler On $B_2$-groups by L. Bican Decompositions of almost completely decomposable Abelian groups by E. A. Blagoveshchenskaya and A. Mader On the divisible parts of quotient groups by A. Blass Minimal rings, central idempotents and the Pierce sheaf by W. D. Burgess On endomorphisms and automorphisms of some pure subgroups of the Baer-Specker group by A. L. S. Corner and B. Goldsmith A combinatorial principle equivalent to the existence of non-free Whitehead groups by P. C. Eklof and S. Shelah Endomorphisms of local Warfield groups by S. T. Files Finitely presented modules over the ring of universal numbers by A. A. Fomin A survey of Butler groups of infinite rank by L. Fuchs Unions of chains of Butler groups by L. Fuchs and K. M. Rangaswamy Some torsion-free groups arising in measure theory by R. G. Gobel and R. M. Shortt Numerical invariants for a class of Butler groups by H. P. Goeters, W. Ullery, and C. Vinsonhaler $K_0$ of regular rings with bounded index of nilpotence by K. R. Goodearl Torsion in quotients of the multiplicative group of a number field by D. Holley and R. Wiegand On $p^\alpha$-injective Abelian groups by P. Keef Abelian groups with contractions I by F.-V. Kuhlmann Typesets and cotypesets of finite-rank torsion-free Abelian groups by R. S. Lafleur A generalization of Butler groups by A. Mader, O. Mutzbauer, and K. M. Rangaswamy Endomorphisms over incomplete discrete valuation rings by W. May $Bext^2(G,T)$ can be nontrivial even assuming GCH by M. Magidor and S. Shelah Representations and duality by R. Mines, C. Vinsonhaler, and W. J. Wickless Extending a splitting criterion on mixed modules by O. Mutzbauer and E. Toubassi Direct summands of $Z^\kappa$ for large $\kappa$ by J. D. O'Neill Abelian groups as noetherian modules over their endomorphism rings by A. T. Paras Isomorphism of Butler groups at a prime by F. Richman The braid group action on the set of exceptional sequences of a hereditary Artin algebra by C. M. Ringel Direct limits of two-dimensional prime spectra by C. Rotthaus and S. Wiegand When is an Abelian $p$-group determined by the Jacobson radical of its endomorphism ring? by P. Schultz Similarities and differences between Abelian groups and modules over non-perfect rings by J. Trlifaj A functor from mixed groups to torsion-free groups by W. J. Wickless A characterization of a class of Butler groups II by P. D. Yom.