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Michiel Hazewinkel, Nadiya Gubareni, V.V. Kirichenko, ""

The text of the first volume of the book covers the major topics in ring and module theory and includes both fundamental classical results and more recent developments. The basic tools of investigation are methods from the theory of modules, which allow a very simple and clear approach both to classical and new results. An unusual main feature of this book is the use of the technique of quivers for studying the structure of rings. A considerable part of the first volume of the book is devoted to a study of special classes of rings and algebras, such as serial rings, hereditary rings, semidistributive rings and tiled orders. Many results of this text until now have been available in journal articles only.

This book is aimed at graduate and post-graduate students and for all mathematicians who use algebraic techniques in their work.

This is a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and algebras and is suitable for independent study

From the reviews of the first edition:

"This is the first of two volumes which aim to take the theory of associative rings and their modules from fundamental definitions to the research frontier. The book is written at a level intended to be accessible to students who have taken standard basic undergraduate courses in linear algebra and abstract algebra. has been written with considerable attention to accuracy, and has been proofread with care. A very welcome feature is the substantial set of bibliographic and historical notes at the end of each chapter." (Kenneth A. Brown, Mathematical Reviews, 2006a)

"This book follows in the footsteps of the valuable work done during the seventies of systematizing the investigation of properties and structure of rings by using their categories of modules. A remarkable novelty in the present monograph is the study of semiperfect rings by means of quivers. Another good idea is the inclusion of the study of commutative as well as non-commutative discrete valuation rings. Each chapter ends with some illustrative historical notes." (José Gómez Torrecillas, Zentralblatt MATH, Vol. 1086 (12), 2006)

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