| Endomorphism Rings of Abelian Groups Softcover Repri Edition Contributor(s): Krylov, P. a. (Author), Mikhalev, Alexander V. (Author), Tuganbaev, A. a. (Author) |
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ISBN: 9048163498 ISBN-13: 9789048163496 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - General - Mathematics | Group Theory - Mathematics | Algebra - Abstract |
| Dewey: 512.2 |
| Series: Algebra and Applications |
| Physical Information: 0.92" H x 6.69" W x 9.61" (1.59 lbs) 443 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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]. |