Ebook: Abelian Groups and Modules: International Conference in Dublin, August 10–14, 1998

This volume contains the refereed proceedings of the International Conference on Abelian Groups and Modules held at the Dublin Institute of Technology in Ireland, from August 10 until August 14, 1998. The meeting brought together more than 50 researchers and graduate students from 14 countries around the world. In a series of eight invited survey talks, experts in the field presented several active areas of research, including:

· Almost completely decomposable abelian groups, Butler groups and almost free groups – the classification problem, and invariants of special classes of torsion-free abelian groups.
· Totally projective groups, their automorphism groups and their group rings – questions about unique passage between these categories.
· Radicals commuting with products.
· The Ziegler spectra of Neumann regular rings and the class (semi-) groups of Prüfer domains.
· The Krull-Schmidt property for valuation domains.

These main talks were accompanied by many other presentations of current research on abelian groups and modules. Methods from model theory, category theory, infinite combinatorics, representation theory, classical algebra and geometry were applied to the study of abelian groups and modules; conversely, results and methods from abelian group theory were applied to general module theory and non-commutative groups.

All this is reflected in the 30 articles in this volume, which introduce the reader to an active and attractive part of algebra that over the years has gained much from its position at the crossroads of mathematics. Lively discussions at the conference influenced the final work on the presented papers, which convey some sense of the intellectual ferment they generated and stimulate the reader to consider and actively investigate the topics and problems contained therein.

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Content:
Front Matter....Pages N1-ix
Ross Allen Beaumont July 23, 1914 – September 28, 1996....Pages 1-6
Modular group algebras and simply presented groups....Pages 7-22
Abelian automorphism groups of countable rank....Pages 23-42
Transitivity and full transitivity over subgroups of abelian p-groups....Pages 43-53
Groups acting on modules....Pages 55-73
Some mixed abelian groups as modules over the ring of pseudo—rational numbers....Pages 75-85
The Baer-Kaplansky theorem for direct sums of self-small mixed groups....Pages 87-100
Finite rank Butler groups with small typesets....Pages 101-106
Normal forms of matrices with applications to almost completely decomposable groups....Pages 107-119
Butler modules over 1-dimensional Noetherian domains....Pages 121-134
Completely decomposable summands of almost completely decomposable groups....Pages 135-147
Some matrix rings associated with ACD groups....Pages 149-165
Stacked bases for a pair of homogeneous completely decomposable groups with bounded quotient....Pages 167-190
Separability conditions for vector R-modules....Pages 191-198
Almost disjoint pure subgroups of the Baer-Specker group....Pages 199-209
Abelian groups mapping onto their endomorphism rings....Pages 211-223
Purity and Reid’s theorem....Pages 225-230
Basic subgroups and a freeness criterion for torsion-free abelian groups....Pages 231-239
Absolutely rigid systems and absolutely indecomposable groups....Pages 241-245
Around nonclassifiability for countable torsion free abelian groups....Pages 247-255
On the compact-open topology of Ext(C,A)....Pages 257-268
Direct decompositions of LCA groups....Pages 269-292
Realizing automorphism groups of metabelian groups....Pages 293-299
On the class semigroups of Pr?fer domains....Pages 301-307
Uniform modules, Г-invariants, and Ziegler spectra of regular rings....Pages 309-317
Locally simple objects....Pages 319-326
On purely extending modules....Pages 327-340
The number of submodules....Pages 341-351
Back Matter....Pages 353-358
....Pages 359-368