Perspectives in Ring Theory

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.

Klappentext

Proceedings of the NATO Advanced Research Workshop, Antwerp, Belgium, July 19-29, 1987

Inhalt
I. Work-Shop: Geometry and Invariant Theory of Quivers.- Deformations of Tilting Modules.- Rational Invariants of Quivers and the Ring of Matrix Invariants.- The Hilbert Series of Matrix Concomitants and its Application.- A Theorem on Invariants of Semi-simple Lie Algebras.- Deformations of Algebras and Hochschild Cohomology.- Report and Open Questions from a Work-shop on Geometry and Invariant Theory of Quivers.- II. Work-Shop: Perspectives in Ring Theory.- Automorphisms of Generic 2 × 2 Matrices.- An Example in Central Division Algebras.- Cohomologie Localte et Cohomologie d'Algèbres de Lie.- Noncommutative Valuation Rings.- On Hopf Galois Extensions of Fields and Number Rings.- The Brauer Long Group of ?/2? Dimodule Algebras.- On the Brauer Group and the Cup Product Map.- Group Actions on Module-finite Rings.- Algebraic Conjugacy Classes and Skew Polynomial Rings.- On the Gelfand-Kirillov Dimension of Normal Localizations and Twisted Polynomial Rings.- Goldie Ranks of Prime Polycyclic Crossed Products.- The Gelfand-Kirillov Dimension of Poincaré-Birkhof-Witt Extensions.- The Nulstellensatz and Generic Flatness.- Gelfand-Kirillov Dimension, Hilbert-Samuel Polynomials and Rings of Differential Operators.- Gabriel-Popescu Type Theorems and Graded Modules.- Crossed Products of Hopf Algebras and Eveloping Algebras.- Progress on Some Problems about Group Actions.- A Note on the P.I. Property of Semigroup Algebras.- Invariant Fields of Linear Groups and Division Algebras.- Group Graded Rings, Smash Products and Additive Categories.- Reflexive Auslauder-Reiten Sequences.- Noncommutative Invariant Theory.- The Brauer-Severi Scheme of the Trace Ring of Generic Matrices.- Some Problems on Associative Rings.- Dubrovin Valuation Rings.- Special Monomial Algebras ofFinite Global Dimension.- Index of Definitions.