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＜電子ブック＞
Endomorphism Rings of Abelian Groups / by P.A. Krylov, Alexander V. Mikhalev, A.A. Tuganbaev
(Algebra and Applications. ISSN:21922950 ; 2)

版	1st ed. 2003.
出版者	Dordrecht : Springer Netherlands : Imprint: Springer
出版年	2003
本文言語	英語
大きさ	XII, 443 p : online resource
著者標目	*Krylov, P.A author Mikhalev, Alexander V author Tuganbaev, A.A author SpringerLink (Online service)
件　名	LCSH:Associative rings LCSH:Associative algebras LCSH:Group theory LCSH:Commutative algebra LCSH:Commutative rings FREE:Associative Rings and Algebras FREE:Group Theory and Generalizations FREE:Commutative Rings and Algebras
一般注記	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 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] HTTP:URL=https://doi.org/10.1007/978-94-017-0345-1

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