Maximal Orders

Name: Maximal Orders
Brand: OUP Oxford
SKU: 9780198526735
Price: 28614.0 INR
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by Irving Reiner

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ISBN13: 9780198526735
Binding: Hardcover
Subject: N/A
Publisher: OUP Oxford
Publisher Imprint: OUP Oxford
Publication Date: March 27, 2003
Pages: 410
Original Price: USD 265.0
Language: English
Edition: Reprint
Item Weight: 753 grams
BISAC Subject(s): Algebra / General

About The Book

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.

About The Author

Professor Irving Reiner (1924-1986), was one of the world's leading experts in representation theory. During his life he published more than 80 research papers, four books (including the original issue of Maximal Orders published by Academic Press in 1975) and many research survey articles on topics related to those contained in this text. In 1962 he was the John Simon Guggenheim Fellow and a former editor of the Illinois Journal of Mathematics and a long-time member of the American Mathematical Society.

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