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Endomorphism Rings of Abelian Groups - Algebra and Applications 2 (Hardback)
  • Endomorphism Rings of Abelian Groups - Algebra and Applications 2 (Hardback)

Endomorphism Rings of Abelian Groups - Algebra and Applications 2 (Hardback)

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Hardback 443 Pages / Published: 31/07/2003
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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].

Publisher: Springer-Verlag New York Inc.
ISBN: 9781402014383
Number of pages: 443
Weight: 1800 g
Dimensions: 234 x 156 x 25 mm
Edition: 2003 ed.


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)

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