Collected Works 1999; 1638 pp; hardcover Volume: 10 ISBN10: 0821806793 ISBN13: 9780821806791 List Price: US$334 Member Price: US$267.20 Order Code: CWORKS/10
 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 40year period and for the use of homological methods in algebra, covering both commutative ring theory and artin algebra theory. Readership Graduate students, researchers, and historians interested in commutative rings and algebras. Reviews "One should thank the editors, all of whom 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 Table of Contents Part 1. Chapter I  Homological dimension and local rings
 On the dimension of modules and algebras. III: Global dimension
 Commutator subgroups of free groups
 On the dimension of modules and algebras. VI: Comparison of global and algebra dimension
 On regular group rings
 Homological dimension in local rings
 Homological dimension in noetherian rings. II
 Codimension and multiplicity
 Codimension and multiplicity (corrections)
 Unique factorization in regular local rings
 A remark on a paper of M. Hironaka
Chapter II  Ramification theory
 On ramification theory in noetherian rings
 Maximal orders
 The Brauer group of a commutative ring
 Modules over unramified regular local rings
 On the purity of the branch locus
 Ramification index and multiplicity
 Modules over unramified regular local rings
 Brauer groups of discrete valuation rings
 Galois actions on rings and finite Galois coverings
Chapter III  Functors
 Coherent functors
 Stable equivalence of artin algebras
 Stable equivalence of dualizing \(R\)varieties
 A functorial approach to representation theory
 Adjoint functors and an extension of the Green correspondence for group representations
 \(D\) Trperiodic modules and functors
Chapter IV  Almost split sequences and artin algebras
 Representation dimension of artin algebras
 A characterization of orders of finite lattice type
 Representation theory of artin algebras. I
 Representation theory of artin algebras. II
 Representation theory of artin algebras. III: Almost split sequences
 Large modules over artin algebras
 Representation theory of artin algebras. IV: Invariants given by almost split sequences
 Representation theory of artin algebras. V: Methods for computing almost split sequences and irreducible morphisms
 Representation theory of artin algebras. VI: A functorial approach to almost split sequences
 Representation theory of hereditary artin algebras
 Almost split sequences whose middle term has at most two indecomposable summands
 Relations for Grothendieck groups of artin algebras
Chapter V  Some topics in representation theory
 On a generalized version of the Nakayama conjecture
 Modules with waists
 Modules determined by their composition factors
 Almost split sequences and group rings
 On a theorem of E. Green on the dual of the transpose
Part 2. Chapter VI  Lattices over general orders
 Functors and morphisms determined by objects
 Applications of morphisms determined by modules
 A survey of existence theorems for almost split sequences
Chapter VII  Tilting theory and homologically finite subcategories
 Coxeter functors without diagrams
 Preprojective modules over artin algebras
 Almost split sequences in subcategories
 Applications of contravariantly finite subcategories
 Homological theory of idempotent ideals
Chapter VIII  Almost split sequences and commutative rings
 Isolated singularities and existence of almost split sequences
 Rational singularities and almost split sequences
 Almost split sequences for rational double points
 The CohenMacaulay type of CohenMacaulay rings
 Almost split sequences for CohenMacaulay modules
 The what, where, and why of almost split sequences
 CohenMacaulay modules for graded CohenMacaulay rings and their completions
 Graded modules and their completions
Chapter IX  Grothendieck groups and CohenMacaulay approximations
 Grothendieck groups of algebras and orders
 Grothendieck groups of algebras with nilpotent annihilators
 The homological theory of maximal CohenMacaulay approximations
 Liftings and weak liftings of modules
Chapter X  Relative theory and syzygy modules
 Relative homology and representation theory. I: Relative homology and homologically finite subcategories
 Relative homology and representation theory. II: Relative cotilting theory
 \(k\)Gorenstein algebras and syzygy modules
 Syzygy modules for noetherian rings
