Ebook: 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.

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Content:
Front Matter....Pages i-xvi
Deformations of Tilting Modules....Pages 1-20
Rational Invariants of Quivers and the Ring of Matrixinvariants....Pages 21-29
The Hilbert Series of Matrix Concomitants and its Application....Pages 31-36
A Theorem on Invariants of Semi-Simple Lie Algebras....Pages 37-40
Deformations of Algebras and Hochschild Cohomology....Pages 41-58
Report and Open Questions from a Workshop on Geometry and Invariant Theory of Quivers....Pages 59-68
Automorphisms of Generic 2 by 2 Matrices....Pages 69-83
An Example in Central Division Algebras....Pages 85-92
Cohomologie Locale Et Cohomologie D’algebres De Lie....Pages 93-104
Noncommutative Valuation Rings....Pages 105-115
On Hopf Galois extensions of fields and number rings....Pages 117-128
The Brauer Long group of Z/2 dimodule algebras....Pages 129-133
On the Brauer Group and the Cup Product Map....Pages 135-145
Group Actions on Module-finite Rings....Pages 147-152
Algebraic Conjugacy Classes and Skew Polynomial Rings....Pages 153-203
On the Gelfand-Kirillov Dimension of Normal Localizations and Twisted Polynomial Rings....Pages 205-214
Goldie Ranks of Prime Polycyclic Crossed Products....Pages 215-219
The Gelfand-Kirillov Dimension of Poincare-Birkhoff-Witt Extensions....Pages 221-226
The Nulstellensatz and Generic Flatness....Pages 227-232
Gelfand-Kirillov Dimension, Hilbert-Samuel polynomials and Rings of Differential Operators....Pages 233-238
Gabriel - Popescu Type Theorems and Graded Modules....Pages 239-251
Crossed Products of Hopf Algebras and Enveloping Algebras....Pages 253-268
Progress on Some Problems about Group Actions....Pages 269-274
A Note on the PI-Property of Semigroup Algebras....Pages 275-278
Invariant fields of linear groups and division algebras....Pages 279-297
Group Graded Rings, Smash Products and Additive Categories....Pages 299-310
Reflexive Auslander-Reiten Sequences....Pages 311-320
Noncommutative Invariant Theory....Pages 321-331
The Brauer Severi scheme of the trace ring of generic matrices....Pages 333-338
Some Problems on Associative Rings....Pages 339-357
Dubrovin Valuation Rings....Pages 359-374
Special Monomial Algebras Of Finite Global Dimension....Pages 375-378
Back Matter....Pages 379-382

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Content:
Front Matter....Pages i-xvi
Deformations of Tilting Modules....Pages 1-20
Rational Invariants of Quivers and the Ring of Matrixinvariants....Pages 21-29
The Hilbert Series of Matrix Concomitants and its Application....Pages 31-36
A Theorem on Invariants of Semi-Simple Lie Algebras....Pages 37-40
Deformations of Algebras and Hochschild Cohomology....Pages 41-58
Report and Open Questions from a Workshop on Geometry and Invariant Theory of Quivers....Pages 59-68
Automorphisms of Generic 2 by 2 Matrices....Pages 69-83
An Example in Central Division Algebras....Pages 85-92
Cohomologie Locale Et Cohomologie D’algebres De Lie....Pages 93-104
Noncommutative Valuation Rings....Pages 105-115
On Hopf Galois extensions of fields and number rings....Pages 117-128
The Brauer Long group of Z/2 dimodule algebras....Pages 129-133
On the Brauer Group and the Cup Product Map....Pages 135-145
Group Actions on Module-finite Rings....Pages 147-152
Algebraic Conjugacy Classes and Skew Polynomial Rings....Pages 153-203
On the Gelfand-Kirillov Dimension of Normal Localizations and Twisted Polynomial Rings....Pages 205-214
Goldie Ranks of Prime Polycyclic Crossed Products....Pages 215-219
The Gelfand-Kirillov Dimension of Poincare-Birkhoff-Witt Extensions....Pages 221-226
The Nulstellensatz and Generic Flatness....Pages 227-232
Gelfand-Kirillov Dimension, Hilbert-Samuel polynomials and Rings of Differential Operators....Pages 233-238
Gabriel - Popescu Type Theorems and Graded Modules....Pages 239-251
Crossed Products of Hopf Algebras and Enveloping Algebras....Pages 253-268
Progress on Some Problems about Group Actions....Pages 269-274
A Note on the PI-Property of Semigroup Algebras....Pages 275-278
Invariant fields of linear groups and division algebras....Pages 279-297
Group Graded Rings, Smash Products and Additive Categories....Pages 299-310
Reflexive Auslander-Reiten Sequences....Pages 311-320
Noncommutative Invariant Theory....Pages 321-331
The Brauer Severi scheme of the trace ring of generic matrices....Pages 333-338
Some Problems on Associative Rings....Pages 339-357
Dubrovin Valuation Rings....Pages 359-374
Special Monomial Algebras Of Finite Global Dimension....Pages 375-378
Back Matter....Pages 379-382
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