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Endomorphism Rings of Abelian Groups: Algebra and Applications, cartea 2

Autor P.A. Krylov, Alexander V. Mikhalev, A.A. Tuganbaev
en Limba Engleză Hardback – 31 iul 2003
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].
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Specificații

ISBN-13: 9781402014383
ISBN-10: 1402014384
Pagini: 456
Ilustrații: XII, 443 p.
Dimensiuni: 156 x 234 x 30 mm
Greutate: 0.81 kg
Ediția:2003
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Algebra and Applications

Locul publicării:Dordrecht, Netherlands

Public țintă

Research

Cuprins

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.

Recenzii

From the reviews:
"In this book, the variety of methods, the beauty of the results, and the appeal of the open problems provide ample justification for the author’s rationale. … book is largely self-contained … . Helpful and challenging sets of exercises appear at the end of each section and open problems are listed at the end of each chapter. This work will be valuable as a text book for a graduate course, a reference on a lively area of mathematics, and a guide to appealing research problems." (Charles Vinsonhaler, Zentralblatt MATH, Vol. 1044 (19), 2004)

Notă biografică

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.