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Endomorphism Rings of Abelian Groups

  • Piotr A. Krylov
  • Alexander V. Mikhalev
  • Askar A. Tuganbaev

Part of the Algebras and Applications book series (AA, volume 2)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev
    Pages 1-64
  3. Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev
    Pages 65-98
  4. Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev
    Pages 99-134
  5. Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev
    Pages 135-180
  6. Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev
    Pages 181-252
  7. Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev
    Pages 253-370
  8. Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev
    Pages 371-412
  9. Back Matter
    Pages 413-443

About this book

Introduction

Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomor­ phism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information about Abelian groups themselves, to introduce new concepts and methods, and to find new interesting classes of groups; second, it stimulates further develop­ ment of the theory of modules and their endomorphism rings. The theory of endomorphism rings can also be useful for studies of the structure of additive groups of rings, E-modules, and homological properties of Abelian groups. The books of Baer [52] and Kaplansky [245] have played an important role in the early development of the theory of endomorphism rings of Abelian groups and modules. Endomorphism rings of Abelian groups are much stu­ died in monographs of Fuchs [170], [172], and [173]. Endomorphism rings are also studied in the works of Kurosh [287], Arnold [31], and Benabdallah [63].

Keywords

Abelian group algebra endomorphism ring torsion

Authors and affiliations

  • Piotr A. Krylov
    • 1
  • Alexander V. Mikhalev
    • 2
  • Askar A. Tuganbaev
    • 3
  1. 1.Tomsk State UniversityTomskRussia
  2. 2.Moscow State UniversityMoscowRussia
  3. 3.Moscow Power Engineering InstituteTechnological UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0345-1
  • Copyright Information Springer Science+Business Media B.V. 2003
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6349-6
  • Online ISBN 978-94-017-0345-1
  • Series Print ISSN 1572-5553
  • Series Online ISSN 2192-2950
  • Buy this book on publisher's site