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Maximal orders / I. Reiner.
Math/Physics/Astronomy Library QA247 .R43 2003
Available
- Format:
- Book
- Author/Creator:
- Reiner, Irving.
- Series:
- London Mathematical Society monographs ; new ser., no. 28.
- London Mathematical Society monographs ; new ser., 28
- Language:
- English
- Subjects (All):
- Ideals (Algebra).
- Algebraic fields.
- Rings (Algebra).
- Physical Description:
- xiii, 395 pages : illustrations ; 25 cm.
- Place of Publication:
- Oxford : Clarendon Press ; New York : Oxford University Press, 2003.
- Contents:
- 1 Algebraic preliminaries
- 1 Integral closure 1
- 2 Homological algebra 8
- 3 Localization 30
- 4 Dedekind domains 44
- 5 Completions and valuations 67
- 6 Radicals of rings 77
- 7 Semisimple rings and simple algebras 90
- 2 Orders
- 9 Reduced norms and traces 112
- 10 Existence of maximal orders; discriminants 125
- 11 Localization of orders 131
- 3 Maximal orders in skewfields (local case)
- 12 Uniqueness of maximal orders 135
- 13 Ramification index; inertial degree 138
- 14 Finite residue class field case 143
- 4 Morita equivalence
- 15 Progenerators 154
- 16 Morita correspondence 161
- 5 Maximal orders over discrete valuation rings
- 17 Maximal orders (complete local case) 170
- 18 Maximal orders (local case) 174
- 19 Ideals 181
- 20 Different, discriminant 184
- 6 Maximal orders over Dedekind domains
- 21 Basic results 187
- 22 Ideal theory 190
- 23 Alternate approach to global ideal theory 204
- 24 Norms of ideals 210
- 25 Different, discriminant 217
- 26 Ideal classes; Jordan-Zassenhaus theorem 224
- 27 Genus 232
- 7 Crossed-product algebras
- 28 Brauer groups 237
- 29 Crossed-product algebras 241
- 30 Cyclic algebras 259
- 31 Cyclic algebras over local fields 263
- 8 Simple algebras over global fields
- 32 Splitting of simple algebras 272
- 33 Reduced norms 282
- 34 Eichler's Theorem 292
- 35 Ideal class groups 306
- 36 K[subscript 0] of maximal orders 314
- 37 Picard groups 319
- 38 Non-maximal orders 340
- 9 Hereditary orders
- 39 Local theory of hereditary orders 351
- 40 Global theory of hereditary orders 367
- 41 Group rings 379.
- Notes:
- Originally published: London : Academic Press, 1975.
- Includes bibliographical references (pages 387-390) and index.
- ISBN:
- 0198526733
- OCLC:
- 51445616
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