Algebra and Geometry
This volume contains five review articles, three in the Al gebra part and two in the Geometry part, surveying the fields of ring theory, modules, and lattice theory in the former, and those of integral geometry and differential-geometric methods in the c
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MATHEMATICS Volume 12
Algebra and Geometry
PROGRESS IN MATHEMATICS
Translations of /togi Nauki - Seriya Matematika 1968: Volume 1 - Mathematical Analysis Volume 2 - Mathematical Analysis 1969: Volume 3 - Probability Theory, Mathematical Statistics, and Theoretical Cybernetics Volume 4 - Mathematical Analysis Volume 5 - Algebra 1970: Volume 6 - Topology and Geometry Volume 7 - Probability Theory, Mathematical Statistics, and Theoretical Cybernetics Volume 8 - Mathematical Analysis 1971: Volume 9 - Algebra and Geometry Volume 10 - Mathematical Analysis Volume 11 - Probability Theory, Mathematical Statistics, and Theoretical Cybernetics Volume 12 - Algebra and Geometry In preparation: Volume 13 - Probability Theory, Mathematical Statistics, and Theoretical Cybernetics Volume 14 - Algebra, Topology, and Geometry Volume 15 - Mathematical Analysis
PROGRESS IN
MATHEMATICS Volume 12
Algebra and Geometry Edited by
R. V. Gamkrelidze
v. A. Steklov Mathematics Institute Academy of Sciences of the USSR, Moscow
Translated from Russian by Nasli H. Choksy
g:>PLENUM PRESS • NEW YORK-LONDON • 1972
The original Russian text was published for the All-Union Institute of Scientific and Technical Information in Moscow in 1970 as a volume of /togi Nauki - Seriya Maternatika EDITORIAL BOARD R. V. Gamkrelidze, Editor-in-Chief N. M. Ostianu, Secretary P. S. Aleksandrov Yu. V. Linnik N. G. Chudakov E. F. Mishchenko M. K. Kerimov M. A. Naimark S. M. Nikol'skii A. N. Kolmogorov L. D. Kudryavtsev N. Kh. Rozov G. F. Laptev K. A. Rybnikov
Library of Congress Catalog Card Number 67-27902 ISBN 978-1-4757-0509-6 ISBN 978-1-4757-0507-2 (eBook) DOI 10.1007/978-1-4757-0507-2 The present translation is published under an agreement with Mezhdunarodnaya Kniga, the Soviet book export agency © 1972 Plenum Press, New York Softcover reprint of the hardcover I st edition 1972 A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011
United Kingdom edition published by Plenum Press, London A Division of Plenum Publishing Company, Ltd. Davis House (4th Floor), 8 Scrubs Lane, Harlesden, NWIO 6SE, England All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher
PREFACE This volume contains five review articles, three in the Algebra part and two in the Geometry part, surveying the fields of ring theory, modules, and lattice theory in the former, and those of integral geometry and differential-geometric methods in the calculus of variations in the latter. The literature covered is primarily that published in 1965-1968.
v
CONTENTS ALGEBRA RING THEORY L. A. Bokut', K. A. Zhevlakov, and E. N. Kuz'min Associative Rings. . . . . . . . . . . . . . . . Lie Algebras and Their Generalizations. ~ 3. Alternative and Jordan Rings. . . . . . . . Bibliography. . . . . . . . . . . . . . . . . . . . . . . .
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3 13 18 25
§
1. Radicals. . . . . . . . . . . . . . . . . . . 2. Projection, Injection, etc. . . . . . . . . . . . . . . . . .. § 3.
