Methods of Graded Rings
The topic of this book, graded algebra, has developed in the past decade to a vast subject with new applications in noncommutative geometry and physics. Classical aspects relating to group actions and gradings have been complemented by new insights stemmi
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Constantin Nˇastˇasescu Freddy Van Oystaeyen
Methods of Graded Rings
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Authors Constantin Nˇastˇasescu Faculty of Mathematics University of Bucharest Str. Academiei 14 70609 Bucharest, Romania e-mail: [email protected] Freddy Van Oystaeyen Department of Mathematics and Computer Science University of Antwerp Middelheimlaan 1 2020 Antwerp, Belgium e-mail: [email protected]
Cataloging-in-Publication Data available Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
Mathematics Subject Classification (2000): 16-XX, 20-XX, 18-XX, 81R30 ISSN 0075-8434 ISBN 3-540-20746-5 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag is a part of Springer Science+Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2004 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10977163
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Acknowledgement A part of this work was done while the first author visited the Flemish Royal Academy as a VLAC-fellow in 2000-2001. Moreover exchange visits for both authors took place in the framework of the bilateral project of the Flemish and Romanian governments. We also thank S. Dascalescu for his collaboration in writing Chapter 9. Finally we thank the referee for careful reading of the manuscript, his suggestions certainly enhanced the presentation of the material. In preparing the text we acknowledge the help of Crina Boboc, C. Calinescu, M. Iovanov, S. Dascalescu, Blas Torrecillas, and J. Gomez-Torrecillas, and Francine Schoeters for typing the final version.
Dedication We dedicate this book our dear wives : Petruta and Danielle ! They allowed us to spend some “quality time” on this book, and even supported our efforts in this.
Introduction The aim of this book is to provide a survey of algebraic methods useful in the investigation of the structure of graded rings and their modules. The concept of gradation is strongly linked to the notion of d
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