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Infinite Abelian Groups
Contributor(s): Kaplansky, Irving (Author)

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ISBN: 0486828506     ISBN-13: 9780486828503
Publisher: Dover Publications
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Binding Type: Paperback - See All Available Formats & Editions
Published: December 2018
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Additional Information
BISAC Categories:
- Mathematics | Algebra - Abstract
- Mathematics | Group Theory
Dewey: 512.25
LCCN: 2018011854
Series: Dover Books on Mathematics
Physical Information: 0.2" H x 5.9" W x 8.9" L (0.30 lbs) 112 pages
Features: Bibliography, Index, Price on Product
 
Descriptions, Reviews, Etc.
Publisher Description:
In the Introduction to this concise monograph, the author states his two main goals: first, "to make the theory of infinite abelian groups available in a convenient form to the mathematical public; second, to help students acquire some of the techniques used in modern infinite algebra." Suitable for advanced undergraduates and graduate students in mathematics, the text requires no extensive background beyond the rudiments of group theory.
Starting with examples of abelian groups, the treatment explores torsion groups, Zorn's lemma, divisible groups, pure subgroups, groups of bounded order, and direct sums of cyclic groups. Subsequent chapters examine Ulm's theorem, modules and linear transformations, Banach spaces, valuation rings, torsion-free and complete modules, algebraic compactness, characteristic submodules, and the ring of endomorphisms. Many exercises appear throughout the book, along with a guide to the literature and a detailed bibliography.
 
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