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Endomorphism Rings of Abelian Groups

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ISBN-10: 1402014384

ISBN-13: 9781402014383

Edition: 2003

Authors: Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev, A. A. Tuganbaev

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This is a monograph on the theory of endomorphism rings of Abelian groups. The theory is a rapidly developing area of algebra and has its origin in the theory of operators of vector spaves. The text contains information on groups themselves, introducing new concepts, methods, and classes of groups.
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Book details

Copyright year: 2003
Publisher: Springer Netherlands
Publication date: 7/31/2003
Binding: Hardcover
Pages: 443
Size: 6.14" wide x 9.21" long x 0.75" tall
Weight: 3.960
Language: English

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.

General Results on Endomorphism Rings
Rings, Modules, and Categories
Abelian Groups
Examples and Some Properties of Endomorphism Rings
Torsion-Free Rings of Finite Rank
Quasi-Endomorphism Rings of Torsion-Free Groups
E-Modules and E-Rings
Torsion-Free Groups Coinciding with Their Pseudo-Socles
Irreducible Torsion-Free Groups
Groups as Modules over Their Endomorphism Rings
Endo-Artinian and Endo-Noetherian Groups
Endo-Flat Primary Groups
Endo-Finite Torsion-Free Groups of Finite Rank
Endo-Projective and Endo-Generator Torsion-Free Groups of Finite Rank
Endo-Flat Torsion-Free Groups of Finite Rank
Ring Properties of Endomorphism Rings
The Finite Topology
Endomorphism Rings with the Minimum Condition
Hom(A, B) as a Noetherian Module over End(B)
Mixed Groups with Noetherian Endomorphism Rings
Regular Endomorphism Rings
Commutative and Local Endomorphism Rings
The Jacobson Radical of the Endomorphism Ring
The Case of p-groups
The Radical of the Endomorphism Ring of a Torsion-Free Group of Finite Rank
The Radical of the Endomorphism Ring of Algebraically Compact and Completely Decomposable Torsion-Free Groups
The Nilpotence of the Radicals N (End(G)) and J (End(G))
Isomorphism and Realization Theorems
The Baer-Kaplansky Theorem
Continuous and Discrete Isomorphisms of Endomorphism Rings
Endomorphism Rings of Groups with Large Divisible Subgroups
Endomorphism Rings of Mixed Groups of Torsion-Free Rank 1
The Corner Theorem on Split Realization
Realizations for Endomorphism Rings of Torsion-Free Groups
The Realization Problem for Endomorphism Rings of Mixed Groups
Hereditary Endomorphism Rings
Self-Small Groups
Categories of Groups and Modules over Endomorphism Rings
Faithful Groups
Faithful Endo-Flat Groups
Groups with Right Hereditary Endomorphism Rings
Groups of Generalized Rank 1
Torsion-Free Groups with Hereditary Endomorphism Rings
Maximal Orders as Endomorphism Rings
p-Semisimple Groups
Fully Transitive Groups
Homogeneous Fully Transitive Groups
Groups whose Quasi-Endomorphism Rings are Division Rings
Fully Transitive Groups Coinciding with Their Pseudo-Socles
Fully Transitive Groups with Restrictions on Element Types
Torsion-Free Groups of p-Ranks [less than or equal] 1