Overview
- Highlights the importance of homological algebra and set theory in the modern theory of abelian groups
- Exposes the reader to the key ideas and modern methods of the subject
- Provides a convenient reference for results scattered throughout the literature
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (18 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 un decidability problems. The treatment of the latter trend includes Shelah’s seminal work on the un decidability 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.
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Bibliographic Information
Book Title: Abelian Groups
Authors: László Fuchs
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-19422-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-19421-9Published: 18 December 2015
Softcover ISBN: 978-3-319-79276-7Published: 21 March 2019
eBook ISBN: 978-3-319-19422-6Published: 12 December 2015
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XXI, 747
Topics: Group Theory and Generalizations, Commutative Rings and Algebras, Category Theory, Homological Algebra