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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, Essen, Germany
K. M. Rangaswamy :  University of Colorado, Colorado Springs, CO
P. Schultz :  The University of Western Australia, Nedlands, Australia
C. Vinsonhaler :  University of Connecticut, Storrs, CT
Abelian Groups, Rings and Modules
eBook ISBN:  978-0-8218-7863-7
Product Code:  CONM/273.E
List Price: $12.00
MAA Member Price: $10.80
AMS Member Price: $9.60
Add to cart
Abelian Groups, Rings and Modules
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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, Essen, Germany
K. M. Rangaswamy :  University of Colorado, Colorado Springs, CO
P. Schultz :  The University of Western Australia, Nedlands, Australia
C. Vinsonhaler :  University of Connecticut, Storrs, CT
eBook ISBN:  978-0-8218-7863-7
Product Code:  CONM/273.E
List Price: $12.00
MAA Member Price: $10.80
AMS Member Price: $9.60
Add to cart
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 273; 2001; 308 pp
    MSC: Primary 05; 06; 13; 15; 16; 20

    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
     
     
    • Part I. Introduction [ MR 1817145 ]
    • Luigi Salce — László Fuchs and his “moddom” work [ MR 1817146 ]
    • Part II. Survey Articles [ MR 1817145 ]
    • A. V. Kelarev and P. Solé — Error-correcting codes as ideals in group rings [ MR 1817147 ]
    • Bruce Olberding — Homomorphisms and duality for torsion-free modules [ MR 1817148 ]
    • K. C. O’Meara and C. Vinsonhaler — Generalizations of isomorphism in torsion-free abelian groups [ MR 1817149 ]
    • Phill Schultz — Automorphism groups of abelian groups [ MR 1817150 ]
    • Part III. Contributed Papers [ MR 1817145 ]
    • David M. Arnold — Direct sum decompositions of torsion-free abelian groups of finite rank [ MR 1817151 ]
    • Maria Alicia Aviñó and Phill Schultz — The endomorphism ring of a bounded abelian $p$-group [ MR 1817152 ]
    • E. Blagoveshchenskaya, G. Ivanov and P. Schultz — The Baer-Kaplansky theorem for almost completely decomposable groups [ MR 1817153 ]
    • Andreas Blass and John Irwin — Maximal pure independent sets [ MR 1817154 ]
    • Dikran Dikranjan and Michael Tkachenko — Characterization of the tori via density of the solution set of linear equations [ MR 1817155 ]
    • Alexander A. Fomin — Quotient divisible mixed groups [ MR 1817156 ]
    • Laszlo Fuchs and Sang Bum Lee — Stacked bases over $h$-local Prüfer domains [ MR 1817157 ]
    • Anthony J. Giovannitti — Groups with locally defined heights and products of $\mathfrak {R}^\ast $ groups [ MR 1817158 ]
    • Rüdiger Göbel and Saharon Shelah — Reflexive subgroups of the Baer-Specker group and Martin’s axiom [ MR 1817159 ]
    • Paul Hill, Charles Megibben and William Ullery — $\Sigma $-isotype subgroups of local $k$-groups [ MR 1817160 ]
    • George Ivanov — Character modules and endomorphism rings of modules over Artinian serial rings [ MR 1817161 ]
    • Peter Loth — Topologically pure extensions [ MR 1817162 ]
    • N. R. McConnell and T. Stokes — Rings having simple adjoint semigroup [ MR 1817163 ]
    • A. Mader, L. G. Nongxa and M. A. Ould-Beddi — Invariants of global crq-groups [ MR 1817164 ]
    • Vahagn H. Mikaelian — On varieties of groups generated by wreath products of abelian groups [ MR 1817165 ]
    • Otto Mutzbauer — Existence of rigid indecomposable almost completely decomposable groups [ MR 1817166 ]
    • W. K. Nicholson and M. F. Yousif — C2-rings and the FGF-conjecture [ MR 1817167 ]
    • Barbara L. Osofsky — Lifting direct sum decompositions of bounded abelian $p$-groups [ MR 1817168 ]
    • K. M. Rangaswamy — On modules and submodules with finite projective dimension [ MR 1817169 ]
    • Lutz Strüngmann and Simone L. Wallutis — On the torsion groups in cotorsion classes [ MR 1817170 ]
    • Jan Trlifaj — Cotorsion theories induced by tilting and cotilting modules [ MR 1817171 ]
    • Jan Žemlička — Steadiness is tested by a single module [ MR 1817172 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Contemporary Mathematics
Volume: 273; 2001; 308 pp
MSC: Primary 05; 06; 13; 15; 16; 20

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.
  • Part I. Introduction [ MR 1817145 ]
  • Luigi Salce — László Fuchs and his “moddom” work [ MR 1817146 ]
  • Part II. Survey Articles [ MR 1817145 ]
  • A. V. Kelarev and P. Solé — Error-correcting codes as ideals in group rings [ MR 1817147 ]
  • Bruce Olberding — Homomorphisms and duality for torsion-free modules [ MR 1817148 ]
  • K. C. O’Meara and C. Vinsonhaler — Generalizations of isomorphism in torsion-free abelian groups [ MR 1817149 ]
  • Phill Schultz — Automorphism groups of abelian groups [ MR 1817150 ]
  • Part III. Contributed Papers [ MR 1817145 ]
  • David M. Arnold — Direct sum decompositions of torsion-free abelian groups of finite rank [ MR 1817151 ]
  • Maria Alicia Aviñó and Phill Schultz — The endomorphism ring of a bounded abelian $p$-group [ MR 1817152 ]
  • E. Blagoveshchenskaya, G. Ivanov and P. Schultz — The Baer-Kaplansky theorem for almost completely decomposable groups [ MR 1817153 ]
  • Andreas Blass and John Irwin — Maximal pure independent sets [ MR 1817154 ]
  • Dikran Dikranjan and Michael Tkachenko — Characterization of the tori via density of the solution set of linear equations [ MR 1817155 ]
  • Alexander A. Fomin — Quotient divisible mixed groups [ MR 1817156 ]
  • Laszlo Fuchs and Sang Bum Lee — Stacked bases over $h$-local Prüfer domains [ MR 1817157 ]
  • Anthony J. Giovannitti — Groups with locally defined heights and products of $\mathfrak {R}^\ast $ groups [ MR 1817158 ]
  • Rüdiger Göbel and Saharon Shelah — Reflexive subgroups of the Baer-Specker group and Martin’s axiom [ MR 1817159 ]
  • Paul Hill, Charles Megibben and William Ullery — $\Sigma $-isotype subgroups of local $k$-groups [ MR 1817160 ]
  • George Ivanov — Character modules and endomorphism rings of modules over Artinian serial rings [ MR 1817161 ]
  • Peter Loth — Topologically pure extensions [ MR 1817162 ]
  • N. R. McConnell and T. Stokes — Rings having simple adjoint semigroup [ MR 1817163 ]
  • A. Mader, L. G. Nongxa and M. A. Ould-Beddi — Invariants of global crq-groups [ MR 1817164 ]
  • Vahagn H. Mikaelian — On varieties of groups generated by wreath products of abelian groups [ MR 1817165 ]
  • Otto Mutzbauer — Existence of rigid indecomposable almost completely decomposable groups [ MR 1817166 ]
  • W. K. Nicholson and M. F. Yousif — C2-rings and the FGF-conjecture [ MR 1817167 ]
  • Barbara L. Osofsky — Lifting direct sum decompositions of bounded abelian $p$-groups [ MR 1817168 ]
  • K. M. Rangaswamy — On modules and submodules with finite projective dimension [ MR 1817169 ]
  • Lutz Strüngmann and Simone L. Wallutis — On the torsion groups in cotorsion classes [ MR 1817170 ]
  • Jan Trlifaj — Cotorsion theories induced by tilting and cotilting modules [ MR 1817171 ]
  • Jan Žemlička — Steadiness is tested by a single module [ MR 1817172 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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