Infinite Abelian Groups

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BESCHREIBUNG

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.
INFORMATION

VERÖFFENTLICHUNGSDATUM: 19.12.2018

AUTOR: Irving Kaplansky

DATEIGRÖSSE: 7,58 MB

DATEINAME: Infinite Abelian Groups.pdf

HERUNTERLADEN ONLINE LESEN

Infinite abelian groups, whitehead problem and some constructions. Saharon Shelah 1 Israel Journal of Mathematics volume 18, pages 243 - 256 (1974)Cite this article. 267 Accesses. 111 Citations. 4 Altmetric. Metrics details. Abstract. We solve here some problems from Fuchs' book. We show that the answer to Whitehead's problem (for groups of power ℵ 1) is independent from the usual ...

Infinite Abelian Groups, Volume 36, Issue 2 László Fuchs Snippet view - 1970. Infinite Abelian Groups, Volume 36, Issue 1 László Fuchs Snippet view - 1970. Common terms and phrases. abelian groups algebraically compact group assume basic subgroup cardinal numbers Cauchy complete Corollary coset cotorsion group countable cyclic groups defined denote direct decomposition direct limit direct ...

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