登入選單

返回Google圖書搜尋

Infinite Abelian Groups

Irving Kaplansky

出版	Courier Dover Publications, 2018-12-19
主題	Mathematics / Algebra / Abstract
ISBN	04868364529780486836454
URL	http://books.google.com.hk/books?id=CAd_DwAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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.