Infinite Abelian Groups

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.<br>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.