Perspectives in Ring Theory

1. Front Matter

   Pages i-xvi

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2. Work-Shop: Geometry and Invariant Theory of Quivers

   1. Deformations of Tilting Modules

      • Dieter Happel, Mary Schaps

      Pages 1-20

   2. Rational Invariants of Quivers and the Ring of Matrixinvariants

      • Lieven Van Bruyn, Aidan Schofield

      Pages 21-29

   3. The Hilbert Series of Matrix Concomitants and its Application

      • Yasuo Teranishi

      Pages 31-36

   4. A Theorem on Invariants of Semi-Simple Lie Algebras

      • Yasuo Teranishi

      Pages 37-40

   5. Deformations of Algebras and Hochschild Cohomology

      • Mary Schaps

      Pages 41-58

   6. Report and Open Questions from a Workshop on Geometry and Invariant Theory of Quivers

      • M. Schaps

      Pages 59-68

3. Work-Shop : Perspectives in Ring Theory

   1. Automorphisms of Generic 2 by 2 Matrices

      • Jak Alev, Lieven Le Bruyn

      Pages 69-83

   2. An Example in Central Division Algebras

      • S. A. Amitsur

      Pages 85-92

   3. Cohomologie Locale Et Cohomologie D’algebres De Lie

      • Geneviève Barou, Marie-Paule Malliavin

      Pages 93-104

   4. Noncommutative Valuation Rings

      • H. H. Brungs

      Pages 105-115

   5. On Hopf Galois extensions of fields and number rings

      • Lindsay N. Childs

      Pages 117-128

   6. The Brauer Long group of Z/2 dimodule algebras

      • Frank DeMeyer

      Pages 129-133

   7. On the Brauer Group and the Cup Product Map

      • Timothy J. Ford

      Pages 135-145

   8. Group Actions on Module-finite Rings

      • S. Jøndrup

      Pages 147-152

   9. Algebraic Conjugacy Classes and Skew Polynomial Rings

      • T. Y. Lam, André Leroy

      Pages 153-203

   10. On the Gelfand-Kirillov Dimension of Normal Localizations and Twisted Polynomial Rings

       • A. Leroy, J. Matczuk, J. Okninski

       Pages 205-214

   11. Goldie Ranks of Prime Polycyclic Crossed Products

       • Martin Lorenz

       Pages 215-219

   12. The Gelfand-Kirillov Dimension of Poincare-Birkhoff-Witt Extensions

       • J. Matczuk

       Pages 221-226

   13. The Nulstellensatz and Generic Flatness

       • J. C. McConnell, J. C. Robson

       Pages 227-232

This proceedings is composed of the papers resulting from the NATO work-shop "Perspectives in Ring Theory" and the work-shop "Geometry and Invariant The­ ory of Representations of Quivers" . Three reports on problem sessions have been induced in the part corresponding to the work-shop where they belonged. One more report on a problem session, the "lost" problem session, will be published elsewhere eventually. vii Acknowledgement The meeting became possible by the financial support of the Scientific Affairs Division of NATO. The people at this division have been very helpful in the orga­ nization of the meeting, in particular we commemorate Dr. Mario di Lullo, who died unexpectedly last year, but who has been very helpful with the organization of earlier meetings in Ring Theory. For additional financial support we thank the national foundation for scientific research (NFWO), the rector of the University of Antwerp, UIA, and the Belgian Ministry of Education. We also gladly acknowledge support from the Belgian Friends of the Hebrew University and the chairman Prof. P. Van Remoortere who honored Prof. S. Amitsur for his continuous contributions to the mathematical activities at the University of Antwerp. I thank the authors who contributed their paper(s) to this proceedings and the lecturers for their undisposable contributions towards the success of the work-shop. Finally I thank Danielle for allowing me to spoil another holiday period in favor of a congress.

• algebra
• associative ring
• automorphism
• cohomology
• group action
• invariant theory
• lie algebra
• matrices
• matrix
• ring theory
• semigroup

• Department of Mathematics, University of Antwerp, Belgium

  F. Oystaeyen, Lieven Bruyn

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