| Dewey Class |
512.46 |
| Title |
Endomorphism Rings of Abelian Groups ([EBook] /) / by Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev. |
| Author |
Krylov, Piotr A. |
| Added Personal Name |
Mikhalev, Alexander V. author. |
| Tuganbaev, Askar A. author. |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Dordrecht : : Springer Netherlands : : Imprint: Springer, , 2003. |
| Physical Details |
XII, 443 p. : online resource. |
| Series |
Algebras and Applications 1572-5553 ; ; 2 |
| ISBN |
9789401703451 |
| Summary Note |
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].: |
| Contents note |
I. General Results on Endomorphism Rings -- II. Groups as Modules over Their Endomorphism Rings -- III. Ring Properties of Endomorphism Rings -- IV. The Jacobson Radical of the Endomorphism Ring -- V. Isomorphism and Realization Theorems -- VI. Hereditary Endomorphism Rings -- VII. Fully Transitive Groups -- References. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-94-017-0345-1 |
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