Abelian Groups - neues Buch

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ISBN/EAN: 3319194224

ISBN - alternative Schreibweisen:
3-319-19422-4, 978-3-319-19422-6
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: laszlo, fuchs, lászló, kaminski
Titel des Buches: abelian groups, abel

Daten vom Verlag:

Autor/in: László Fuchs
Titel: Springer Monographs in Mathematics; Abelian Groups
Verlag: Springer; Springer International Publishing
747 Seiten
Erscheinungsjahr: 2015-12-12
Cham; CH
Sprache: Englisch
117,69 € (DE)
121,00 € (AT)
136,00 CHF (CH)
Available
XXI, 747 p.

EA; E107; eBook; Nonbooks, PBS / Mathematik/Arithmetik, Algebra; Gruppen und Gruppentheorie; Verstehen; Butler group; abelian group; automorphism group; endomorphism ring; homomorphism groups; torsion; B; Group Theory and Generalizations; Commutative Rings and Algebras; Category Theory, Homological Algebra; Mathematics and Statistics; Algebra; BB

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.

-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.

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.

-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare thereader 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.