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Graded Orders

  • L. le Bruyn
  • M. Van den Bergh
  • F. Van Oystaeyen

Table of contents

  1. Front Matter
    Pages i-vi
  2. L. le Bruyn, M. Van den Bergh, F. Van Oystaeyen
    Pages 1-4
  3. L. le Bruyn, M. Van den Bergh, F. Van Oystaeyen
    Pages 5-36
  4. L. le Bruyn, M. Van den Bergh, F. Van Oystaeyen
    Pages 37-102
  5. L. le Bruyn, M. Van den Bergh, F. Van Oystaeyen
    Pages 103-131
  6. L. le Bruyn, M. Van den Bergh, F. Van Oystaeyen
    Pages 133-173
  7. L. le Bruyn, M. Van den Bergh, F. Van Oystaeyen
    Pages 175-199
  8. Back Matter
    Pages 201-208

About this book

Introduction

In a clear, well-developed presentation this book provides the first systematic treatment of structure results for algebras which are graded by a goup. The fruitful method of constructing graded orders of special kind over a given order, culminating in applications of the construction of generalized Rees rings associated to divisors, is combined with the theory of orders over graded Krull domains. This yields the construction of generalized Rees rings corresponding to the central ramification divisor of the orders and the algebraic properties of the constructed orders. The graded methods allow the study of regularity conditions on order.

The book also touches upon representation theoretic methods, including orders of finite representation type and other aspects of this theory applicable to the classification of orders. The final chapter describes the ring theoretical approach to the classification of orders of global dimension two, originally carried out by M. Artin using more geometrical methods.

Since its subject is important in many research areas, this book will be valuable reading for all researchers and graduate students with an interest in non-commutative algebra.

Keywords

Abelian group algebra commutative algebra finite group torsion

Authors and affiliations

  • L. le Bruyn
    • 1
  • M. Van den Bergh
    • 1
  • F. Van Oystaeyen
    • 1
  1. 1.University of AntwerpAntwerp (Wilrijk)Belgium

Bibliographic information