Overview

This is the first monograph on the theory of endomorphism rings of Abelian groups. The theory is a rapidly developing area of algebra and has its origin in the theory of operators of vector spaves. The text contains additional information on groups themselves, introducing new concepts, methods, and classes of groups. All the main fields of the theory of endomorphism rings of Abelian groups from early results to the most recent are covered. Neighbouring results on endomorphism rings of modules are also mentioned. The text has many pedagogical features: all the necessary definitions and formulations of assertions on Abelian groups, rings, and modules are gathered in the first two sections; summaries of results; exercises of varying difficulty in each section; lesser known facts on rings and modules are presented with proofs; and comments at the end of each chapter together with a brief historical review as well as a look at the future direction of modern research.

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9781402014383

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From the reviews: <p> In this book, the variety of methods, the beauty of the results, and the appeal of the open problems provide ample justification for the authora (TM)s rationale. a ] book is largely self-contained a ] . Helpful and challenging sets of exercises appear at the end of each section and open problems are listed at the end of each chapter. This work will be valuable as a text book for a graduate course, a reference on a lively area of mathematics, and a guide to appealing research problems. (Charles Vinsonhaler, Zentralblatt MATH, Vol. 1044 (19), 2004)

Author Information

Askar Tuganbaev received his Ph.D. at the Moscow State University in 1978 and has been a professor at Moscow Power Engineering Institute (Technological University) since 1978. He is the author of three other monographs on ring theory and has written numerous articles on ring theory.

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