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AMS Chelsea Publishing
1986; 185 pp; hardcover
List Price: US$36
Member Price: US$32.40
Order Code: CHEL/283.H
Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas.
This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients.
A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments.
"An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course] ... in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need. In addition to covering the basic topics ... the author covers some topics not so readily available to the nonspecialist ... the chapters are written to be as independent as possible ... [which will be appreciated by] students making their first acquaintance with the subject ... one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist."
-- American Mathematical Monthly
"An excellent textbook and "classical" reference-text in associative ring theory."
-- Zentralblatt MATH
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