Endomorphism Rings of Abelian Groups (Paperback) (ISBN-13: 9789048163496)

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].

Author: P. a. Krylov, Alexander V. Mikhalev, A. a. Tuganbaev
ISBN-10: 9048163498
ISBN-13: 9789048163496
Publisher: Springer
Language: English
Published: 12/03/2010
Pages: 443
Format: Paperback
Weight: 1.59lbs
Size: 9.61h x 6.69w x 0.92d