Maximal Orders

Name: Maximal Orders
Price: 194.0 USD
Availability: InStock
ISBN: 9780198526735

ISBN-10: 0198526733

ISBN-13: 9780198526735

Edition: 2003

Authors: Irving Reiner

List price: $240.00

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This is a reissue of a classic text, which includes the author's own corrections and provides a very accessible, self contained introduction to the classical theory of orders and maximal orders over a Dedekind ring. It starts with a long chapter that provides the algebraic prerequisites for this theory, covering basic material on Dedekind domains, localizations and completions, as well as semisimple rings and separable algebras. This is followed by an introduction to the basic toolsin studying orders, such as reduced norms and traces, discriminants, and localization of orders. The theory of maximal orders is then developed in the local case, first in a complete setting, and then over any…

Book details

List price: $240.00
Copyright year: 2003
Publisher: Oxford University Press, Incorporated
Publication date: 3/27/2003
Binding: Hardcover
Pages: 410
Size: 6.14" wide x 9.21" long x 1.02" tall
Weight: 1.562
Language: English



Foreword


Preface


Acknowledgements


Permanent notation



Algebraic preliminaries



Integral closure



Homological algebra



Localization



Dedekind domains



Completions and valuations



Radicals of rings



Semisimple rings and simple algebras



Orders



Definitions and examples



Reduced norms and traces



Existence of maximal orders; discriminants



Localization of orders



Maximal orders in skewfields (local case)



Uniqueness of maximal orders



Ramification index; inertial degree



Finite residue class field case



Morita equivalence



Progenerators



Morita correspondence



Maximal orders over discrete valuation rings



Maximal orders (complete local case)



Maximal orders (local case)



Ideals



Different, discriminant



Maximal orders over Dedekind domains



Basic results



Ideal theory



Alternate approach to global ideal theory



Norms of ideals



Different, discriminant



Ideal classes; Jordan-Zassenhaus theorem



Genus



Crossed-product algebras



Brauer groups



Crossed-product algebras



Cyclic algebras



Cyclic algebras over local fields



Simple algebras over global fields



Splitting of simple algebras



Reduced norms



Eichler's Theorem



Ideal class groups



K[subscript 0] of maximal orders



Picard groups



Non-maximal orders



Hereditary orders



Local theory of hereditary orders



Global theory of hereditary orders



Group rings


References


Index