Endomorphism Rings of Abelian Groups

P. A. Krylov

ISBN 10: 9048163498 / ISBN 13: 9789048163496

Editore: Springer Netherlands, 2010

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Druck auf Anfrage Neuware - Printed after ordering - 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].

Codice articolo 9789048163496

Dati bibliografici

• Titolo: Endomorphism Rings of Abelian Groups
• Editore: Springer Netherlands
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 9048163498
• ISBN 13: 9789048163496
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 244 L x 170 A x 25 P (millimetri) 244 millimetri di larghezza per 170 millimetri di altezza per 25 millimetri di profondità
• Peso: 781 grammi

Descrizione articolo

Riassunto

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].

Informazioni sull?autore

Askar Tuganbaev received his Ph.D. at the Moscow State University in 1978 and has been a professor at Moscow Power Engineering Institute (Technological University) since 1978. He is the author of three other monographs on ring theory and has written numerous articles on ring theory.