Lattices over Orders I
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Klaus W. Roggenkamp McGill University, Montreal
Verena Huber - Dyson University of Illinois, Chicago Circle
Lattices over Orders I
Springer-Verlag Berlin· Heidelberg· New York 1970
K. W. Roggenkamy Dept. of Mathematics, McGil University Montreal, P. Q.lCanada (During the preparation of these notes the first author has enjoyed research positions at the University of lIJinois, Universitt de Montrtal and at McGill University.)
v. Huber-Dyson Dept. of Mathematics, University of Illinois Chicago, IL 60680/USA
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re·use of illustrations. broadcasting, reproduction by photocopying machine or $imilar means, and storage in data banks.
Under § ~4 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. Cl by Springer-Verlag Berlin· Heidelberg 1970. Library ofCoDgIl:ss Catalog Card Number 71-108 H4.
Title No. 3271
PREFACE .)
These notes constitute the preliminary version of a book on lattices over orders. This might explain why we have included elementary definitions and theorems, thus deviating from the original character of the LECTURE NOTES. The notes cons1st of two volumes, and to make the first one, wh1ch mainly develops the theory of maximal orders, selfcontained we have included a list of references and an index. Because of the preliminary character of the notes we welcome every suggestion which might improve the later book.
This work 1s an attempt to close the gap between the producing research scientist and the consuming reader. Our own experience has convinced us that our field abounds with "mathematical folklore". The theory of orders is quite essentially based on this kind of common knowledge, especially from related fields, such as algebraic number and class field theory, homological algebra and the theory of algebras. As a matter of fact, the rapid modern development since 1950 employs this type of results as well as many early papers both as tools and as guiding light. Moreover. it seems that this development has reached a certain culminating point with some of the most recent results, and we feel 1t 1s ready for presentation in a reasonably complete form. Thus we are undertaking the task of clarifying the theory of orders eo ipso, of systematizing the wealth of existing and nonexisting literature, and last but not least, to bring into unified form and to moderniZe, where we feel it is necessary, this vast field of knowledge. Apart from this subjective motivation, the book shall serve two -
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in our opinion equally important - purposes. On the one hand it shall )
The authors wish to express their gratitude to all the institutions, that have generously supported this work. Special thanks to Mrs. Betty Kurrle for her gracious assistance with the typing!
IV allow a good student or the eager reader, who is not
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