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Abelian Groups, Rings and Modules
Edited by: A. V. Kelarev, University of Tasmania, Hobart, Tasmania, Australia, R. Göbel, University of Essen, Germany, K. M. Rangaswamy, University of Colorado, Colorado Springs, CO, P. Schultz, The University of Western Australia, Nedlands, Australia, and C. Vinsonhaler, University of Connecticut, Storrs, CT
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Contemporary Mathematics
2001; 308 pp; softcover
Volume: 273
ISBN-10: 0-8218-2751-0
ISBN-13: 978-0-8218-2751-2
List Price: US$91
Member Price: US$72.80
Order Code: CONM/273
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This volume presents the proceedings from the conference on Abelian Groups, Rings, and Modules (AGRAM) held at the University of Western Australia (Perth). Included are articles based on talks given at the conference, as well as a few specially invited papers. The proceedings are dedicated to Professor László Fuchs. The book includes a tribute and a review of his work by his long-time collaborator, Professor Luigi Salce.

Four surveys from leading experts follow Professor Salce's article. They present recent results from active research areas:

  • Error correcting codes as ideals in group rings,
  • Duality in module categories,
  • Automorphism groups of abelian groups, and
  • Generalizations of isomorphism in torsion-free abelian groups.

In addition to these surveys, the volume contains 22 research articles in diverse areas connected with the themes of the conference. The areas discussed include abelian groups and their endomorphism rings, modules over various rings, commutative and non-commutative ring theory, varieties of groups, and topological aspects of algebra. The book offers a comprehensive source for recent research in this active area of study.

Readership

Graduate students and research mathematicians interested in abelian group theory and combinatorics.

Table of Contents

Introduction
  • L. Salce -- László Fuchs and his "moddom" work
Survey articles
  • A. V. Kelarev and P. Solé -- Error-correcting codes as ideals in group rings
  • B. Olberding -- Homomorphisms and duality for torsion-free modules
  • K. C. O'Meara and C. Vinsonhaler -- Generalizations of isomorphism in torsion-free abelian groups
  • P. Schultz -- Automorphism groups of abelian groups
Contributed papers
  • D. M. Arnold -- Direct sum decompositions of torsion-free abelian groups of finite rank
  • M. A. Aviñó and P. Schultz -- The endomorphism ring of a bounded abelian \(p\)-group
  • E. Blagoveshchenskaya, G. Ivanov, and P. Schultz -- The Baer-Kaplansky theorem for almost completely decomposable groups
  • A. Blass and J. Irwin -- Maximal pure independent sets
  • D. Dikranjan and M. Tkachenko -- Characterization of the tori via density of the solution set of linear equations
  • A. A. Fomin -- Quotient divisible mixed groups
  • L. Fuchs and S. B. Lee -- Stacked bases over h-local Prüfer domains
  • A. J. Giovannitti -- Groups with locally defined heights and products of \(\mathfrak{R}^*\) groups
  • R. Göbel and S. Shelah -- Reflexive subgroups of the Baer-Specker group and Martin's axiom
  • P. Hill, C. Megibben, and W. Ullery -- \(\Sigma\)-isotype subgroups of local \(k\)-groups
  • G. Ivanov -- Character modules and endomorphism rings of modules over Artinian serial rings
  • P. Loth -- Topologically pure extensions
  • N. R. McConnell and T. Stokes -- Rings having simple adjoint semigroup
  • A. Mader, L. G. Nongxa, and M. A. Ould-Beddi -- Invariants of global crq-groups
  • V. H. Mikaelian -- On varieties of groups generated by wreath products of abelian groups
  • O. Mutzbauer -- Existence of rigid indecomposable almost completely decomposable groups
  • W. K. Nicholson and M. F. Yousif -- C2-rings and the FGF-conjecture
  • B. L. Osofsky -- Lifting direct sum decompositions of bounded abelian \(p\)-groups
  • K. M. Rangaswamy -- On modules and submodules with finite projective dimension
  • L. Strüngmann and S. L. Wallutis -- On the torsion groups in cotorsion classes
  • J. Trlifaj -- Cotorsion theories induced by tilting and cotilting modules
  • J. Žemlička -- Steadiness is tested by a single module
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