Endomorphism Rings of Abelian Groups 2003 Edition Contributor(s): Krylov, P. a. (Author), Mikhalev, Alexander V. (Author), Tuganbaev, A. a. (Author) |
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ISBN: 1402014384 ISBN-13: 9781402014383 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: July 2003 Annotation: This book is the first monograph on the theory of endomorphism rings of Abelian groups. The theory is a rapidly developing area of algebra and has its origin in the theory of operators of vector spaves. The text contains additional information on groups themselves, introducing new concepts, methods, and classes of groups. All the main fields of the theory of endomorphism rings of Abelian groups from early results to the most recent are covered. Neighbouring results on endomorphism rings of modules are also mentioned. This text has many pedagogical features: -all the necessary definitions and formulations of assertions on Abelian groups, rings, and modules are gathered in the first two sections; |
Additional Information |
BISAC Categories: - Mathematics | Group Theory - Mathematics | Algebra - General - Mathematics | Algebra - Abstract |
Dewey: 512.25 |
LCCN: 2003057307 |
Series: Algebras and Applications |
Physical Information: 1" H x 6.14" W x 9.21" (1.79 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]. |