Nicht aus der Schweiz? Besuchen Sie lehmanns.de
Endomorphism Rings of Abelian Groups - P.A. Krylov, Alexander V. Mikhalev, A.A. Tuganbaev

Endomorphism Rings of Abelian Groups

Buch | Softcover
443 Seiten
2010 | Softcover reprint of the original 1st ed. 2003
Springer (Verlag)
978-90-481-6349-6 (ISBN)
CHF 74,85 inkl. MwSt
Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. 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.
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].

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.

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.

Erscheint lt. Verlag 3.12.2010
Reihe/Serie Algebras and Applications ; 2
Zusatzinfo XII, 443 p.
Verlagsort Dordrecht
Sprache englisch
Maße 170 x 244 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
ISBN-10 90-481-6349-8 / 9048163498
ISBN-13 978-90-481-6349-6 / 9789048163496
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich