Graded Orders

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. L. Le Bruyn, M. Van Den Bergh, F. Van Oystaeyen. Includes Index. Bibliography: P. 201-205. Contents......Page all_3209_to_00212.cpc0003.djvu Introduction......Page all_3209_to_00212.cpc0005.djvu I. Commutative Arithmetical Graded Rings......Page all_3209_to_00212.cpc0009.djvu I.1. Graded Krull Domains......Page all_3209_to_00212.cpc0010.djvu 1.2. Valuations and the structure of Gr-Dedekind Rings......Page all_3209_to_00212.cpc0024.djvu II.1. Graded Rings over Goldie Rings......Page all_3209_to_00212.cpc0041.djvu II.2. Divisorially Graded Rings and Generalized Rees Rings......Page all_3209_to_00212.cpc0048.djvu II.3. Graded Rings Satisfying Polynomial Identities......Page all_3209_to_00212.cpc0056.djvu II.4. Orders and Graded Orders......Page all_3209_to_00212.cpc0063.djvu II.5. Some General Techniques......Page all_3209_to_00212.cpc0085.djvu III.1. Orders Graded by Torsion Free Abelian Groups......Page all_3209_to_00212.cpc0107.djvu III.2. Orders Graded by Finite Groups......Page all_3209_to_00212.cpc0112.djvu III.3. Generalized Crossed Product Azumaya Algebras......Page all_3209_to_00212.cpc0115.djvu III.4. Extensions of Tame Orders and Related Sequences......Page all_3209_to_00212.cpc0122.djvu IV.1. Moderated Gorenstein and Regular Orders......Page all_3209_to_00212.cpc0137.djvu IV.2. Orders of Finite Representation Type......Page all_3209_to_00212.cpc0144.djvu IV.3. Regularizable Domains......Page all_3209_to_00212.cpc0151.djvu IV.4. Smooth Tame Orders......Page all_3209_to_00212.cpc0155.djvu IV.5. Weak Brauer-Severi Schemes......Page all_3209_to_00212.cpc0167.djvu V.1. Introduction......Page all_3209_to_00212.cpc0179.djvu V.2. Rational Double Points Associated to Two-dimensional Tame Orders of Finite Representation Type......Page all_3209_to_00212.cpc0181.djvu V.3. Skew Group Rings and Projective Representations Associated to Two-dimensional Tame Orders of Finite Representation Type......Page all_3209_to_00212.cpc0187.djvu V.4. Classification of Two-dimensional Maximal Orders of Finite Representation Type......Page all_3209_to_00212.cpc0191.djvu V.5. Appendix : Recent Work of I. Reiten and the Second Author......Page all_3209_to_00212.cpc0198.djvu References......Page all_3209_to_00212.cpc0205.djvu Index......Page all_3209_to_00212.cpc0210.djvu