Algebra and Applications

Endomorphism Rings of Abelian Groups

Authors: Krylov, Piotr, Mikhalev, Alexander V., Tuganbaev, Askar

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About this book

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].

About the authors

Askar Tuganbaev received his Ph.D. at the Moscow State University in 1978 and has been a professor at Moscow Power Engineering Institute (Technological University) since 1978. He is the author of three other monographs on ring theory and has written numerous articles on ring theory.

Reviews

From the reviews:

"In this book, the variety of methods, the beauty of the results, and the appeal of the open problems provide ample justification for the author’s rationale. … book is largely self-contained … . Helpful and challenging sets of exercises appear at the end of each section and open problems are listed at the end of each chapter. This work will be valuable as a text book for a graduate course, a reference on a lively area of mathematics, and a guide to appealing research problems." (Charles Vinsonhaler, Zentralblatt MATH, Vol. 1044 (19), 2004)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook 85,59 €
price for Spain (gross)
  • ISBN 978-94-017-0345-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-1-4020-1438-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,99 €
price for Spain (gross)
  • ISBN 978-90-481-6349-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Endomorphism Rings of Abelian Groups
Authors
Series Title
Algebra and Applications
Series Volume
2
Copyright
2003
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-0345-1
DOI
10.1007/978-94-017-0345-1
Hardcover ISBN
978-1-4020-1438-3
Softcover ISBN
978-90-481-6349-6
Series ISSN
1572-5553
Edition Number
1
Number of Pages
XII, 443
Topics