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Dover Books on Mathematics Ser.: Infinite Abelian Groups by Irving Kaplansky (2018, Trade Paperback)

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About this product

Product Identifiers

PublisherDover Publications, Incorporated

ISBN-100486828506

ISBN-139780486828503

eBay Product ID (ePID)16038283691

Product Key Features

Number of Pages112 Pages

LanguageEnglish

Publication NameInfinite Abelian Groups

SubjectGroup Theory, Algebra / Abstract

Publication Year2018

TypeTextbook

AuthorIrving Kaplansky

Subject AreaMathematics

SeriesDover Books on Mathematics Ser.

FormatTrade Paperback

Dimensions

Item Weight5.8 Oz

Item Length9 in

Item Width6 in

Additional Product Features

Intended AudienceTrade

LCCN2018-011854

Dewey Edition23

Dewey Decimal512/.25

Table Of Content1. Introduction 2. Examples of Abelian Groups 3. Torsion Groups 4. Zorn's Lemma 5. Divisible Groups 6. Two Test Problems 7. Pure Subgroups 8. Groups of Bounded Order 9. Height 10. Direct Sums of Cyclic Groups 11. Ulm's Theorem 12. Modules and Linear Transformations 13. Banach Spaces 14. Valuation Rings 15. Torsion-free Modules 16. Complete Modules 17. Algebraic Compactness 18. Characteristic Submodules 19. The Ring of Endomorphisms 20. Notes Bibliography Index

SynopsisThis concise monograph presents the theory of infinite abelian groups in a convenient form and helps students acquire some of the techniques used in modern infinite algebra. 1969 edition., 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.

LC Classification NumberQA171.K35 2018