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Abelian groups

Fuchs, Laszlo.

Abelian groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	Abelian groupsby Laszlo Fuchs.
Author:	Fuchs, Laszlo.
Published:	Cham :Springer International Publishing :2015.
Description:	xxi, 747 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Abelian groups.
Online resource:	http://dx.doi.org/10.1007/978-3-319-19422-6
ISBN:	9783319194226$q(electronic bk.)

Abelian groups
Fuchs, Laszlo.

Abelian groups[electronic resource] /by Laszlo Fuchs. - Cham :Springer International Publishing :2015. - xxi, 747 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

Fundamentals -- Direct Sums -- Direct Sums of Cyclic Groups -- Divisibility and Injectivity -- Purity and Basic Subgroups -- Algebraically Compact Groups -- Homomorphism Groups -- Tensor and Torsion Products -- Groups of Extensions and Cotorsion Groups -- Torsion Groups -- p-Groups with Elements of Infinite Height -- Torsion-free Groups -- Torsion-free Groups of Infinite Rank -- Butler Groups -- Mixed Groups -- Endomorphism Rings -- Automorphism groups -- Groups in Rings and in Fields.

Written by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah's seminal work on the undecidability in ZFC of Whitehead's Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology, and homological algebra. An abundance of exercises are included to test the reader's comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject's further development.

ISBN: 9783319194226$q(electronic bk.)

Standard No.: 10.1007/978-3-319-19422-6doiSubjects--Topical Terms:

245403
Abelian groups.

LC Class. No.: QA180

Dewey Class. No.: 515.25

Abelian groups
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490 1 $a Springer monographs in mathematics, $x 1439-7382
505 0 $a Fundamentals -- Direct Sums -- Direct Sums of Cyclic Groups -- Divisibility and Injectivity -- Purity and Basic Subgroups -- Algebraically Compact Groups -- Homomorphism Groups -- Tensor and Torsion Products -- Groups of Extensions and Cotorsion Groups -- Torsion Groups -- p-Groups with Elements of Infinite Height -- Torsion-free Groups -- Torsion-free Groups of Infinite Rank -- Butler Groups -- Mixed Groups -- Endomorphism Rings -- Automorphism groups -- Groups in Rings and in Fields.
520 $a Written by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah's seminal work on the undecidability in ZFC of Whitehead's Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology, and homological algebra. An abundance of exercises are included to test the reader's comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject's further development.
650 0 $a Abelian groups. $3 245403
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650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Commutative Rings and Algebras. $3 274057
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