Endomorphism Rings of Abelian Groups [electronic resource] /

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].

Bibliographic Details

Main Authors:	Krylov, Piotr A. author., Mikhalev, Alexander V. author., Tuganbaev, Askar A. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Dordrecht : Springer Netherlands : Imprint: Springer, 2003
Subjects:	Mathematics., Associative rings., Rings (Algebra)., Commutative algebra., Commutative rings., Group theory., Associative Rings and Algebras., Group Theory and Generalizations., Commutative Rings and Algebras.,
Online Access:	http://dx.doi.org/10.1007/978-94-017-0345-1
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