Selected Works of Maurice Auslander (Collected Works)

In view of Maurice Auslander's important contributions to many parts of algebra, there is great interest in the present volume. This book features a broad selection of the core of his work, including commutative algebra, singularity theory, the theory of orders, and the representation theory of artin algebras. Although Auslander worked in many areas, there are characteristics common to most of his research. Of particular note is his use of homological methods, including functor categories. While his early work was concerned mostly with commutative rings and his later work mainly with artin algebras, he was always interested in finding common features and common settings. The broad range and impact of Auslander's contributions are reflected clearly in this volume. The editors have included background material, interrelationships between papers and indications of further developments. A paper of note and one that is not available readily is included: the Queen Mary College Notes on ``Representation Dimension of Artin Algebras''. This book is of interest for the historical development of algebra over a 40-year period and for the use of homological methods in algebra, covering both commutative ring theory and artin algebra theory.

One should thank the editors, all of whome were longstanding collaborators of Auslander, for the work involved in editing these volumes. They are a must for any algebraist working in the areas mentioned above to see all the important contributions by Auslander, most of them very timely even today, and some of them more timely than when they were written. Mathematical Reviews