Algebra
all Products
Hardcover Books
Mathematics
Maximal Orders
Maximal Orders
Reiner, Irving
Select Format
Regular price
$250.00 USD
Regular price
$263.16 USD
Sale price
$250.00 USD
Unit price
per
Shipping calculated at checkout.
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 wtih 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 tools in 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 discrete valuation ring. This paves the way to a chapter on the ideal theory in global maximal orders with detailed expositions on ideal classes, the jordan-Zassenhaus Theorum and genera. This is followed by a chapter on Brauer groups and crossed product algebras, where Hasse's theory of cyclic algebras over local fields is presented in a clear and self-contained fashion. Assuming a couple of facts from class field theory, the book goes on to present the theory of simple algebras over global fields covering in particular Eichler's Theorum on the ideal classes in a maximal order, as well as various results on the KO group and Picard group of orders. The rest of the book is devoted to a discussion of non-maximal orders, with particular emphasis on hereditary orders and group rings. The ideas collected in this book have found important applications in the smooth representation theory of reductive p-adic groups. This text provides a useful introduction to this wide range of topics. It is written at a level suitable for beginning postgraduate students, is highly suited to class teaching and provides a wealth of exercises.
Accessories:
No Accessory
Publisher
OXFORD UNIV PR
Bisac Major Subject
Mathematics
Binding Type
Hardcover
Country Of Origin
US
Number Of Units
1
Length
9.21 Inches
Barcode Indicator
ISBN
Width
6.14 Inches
Publication Date
1970-01-01
Height
0.94 Inches
ISBN 10
0198526733
Weight
1.66 Pounds
Book EAN
9780198526735
Target Audiance
Adults
User reviews will be displayed here...
Related products or products you might find interesting
20% OFF
The Bible Recap: Deepen Your Understanding of God's Attributes from Every Book in the Old Testament
Cobble, Tara
$17.21 USD Shop Now
Art & Art Instruction
Art & Art Instruction
20% OFF
Architecture
Window Shopping with Helen Keller: Architecture and Disability in Modern Culture
Serlin, David
$121.96 USD Shop Now
Art & Art Instruction
Biography / Autobiography
Biography / Autobiography
Biography / Autobiography
Tales from the Dancefloor: Manchester / The Warehouse Project / Parklife / Sankeys / The Ha
Lord, Sacha
$30.00 USD Shop Now
Biography / Autobiography