Robert Breckenridge Warfield, Jr. (1940–1989)

Since the publication of the first edition in 1989, this book has been used by several generations of graduate students. From the accumulated comments, it became clear that a number of changes in the presentation of the material would make the book more accessible, particularly to students reading the text on their own. During this same period, the explosive growth of the area of quantum groups provided a large new crop of noetherian rings to be analyzed, and thus gave major impetus to research in noetherian ring theory. While a general development of the theory of quantum groups would not fit into a book of the present scope, many of the basic types of quantum groups are ideally suited as examples on which the concepts and tools developed in the text can be tested. Finally, readers of the first edition found a substantial list of typographical and other minor errors. This revised edition is designed to address all these points. Undoubtedly, however, the retyping of the text in TeX has introduced a new supply of typos for readers' entertainment.

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Changes to the order and emphasis of topics were based, as mentioned, on the combined experience and comments of numerous students and professors who used the first edition over the past 14 years. In particular, more examples and additional manipulations with specific rings – especially in the early part of the book – were requested.