Preface
Permanent Notation
1: Algebraic preliminaries
2: Orders
3: Maximal orders in skewfields (local case)
4: Morita equivilence
5: Maximal orders over discrete valuation rings
6: Maximal orders over Dedekind domains
7: Crossed-product algebras
8: Simple algebras over global fields
9: Hereditary orders
Authors corrections to text
References
Index
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.
Reiner's book provides an excellent introduction for students and serves as an indispensible reference for researchers. Zentralblatt MATH Reiner's book gives by far the most extensive and most readable account available of the classical theory of maximal orders. The book has been written with great care, and is a pleasure to read. Unlike many books at such an advanced level, it contains many interesting exercises, with hints where appropriate. It is essential to the library of every working algebraist. Bulletin of the American Mathematical Society The book certainly fills a gap in the mathematical literature, since no modern text-book on maximal orders has been available. The author has succeeded very well in giving a clear and easily accessible presentation of the subject. Mathematical Reviews
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