Maximal Orders

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 SocietyThe 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`This book is unique in its role of providing a self-contained and easily accessible introduction to the theory of orders and maximal orders in both the local and the global setting. Readers of the book will also find it valuable as a guide to many basic algebraic notions such as localizations, completions, the Jacobson radical, and Morita theory. The text is well-written and complete, and well-chosen exercises are offered at the end of each chapter. Thebook is well-suited as a text for graduate courses in representation theory, and for many years has filled a gap in the literature in the area of orders and maximal orders.‘Professor Tsit-Yuen Lam, University of California at Berkeley.

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-timemember of the American Mathematical Society.