Algebraic Systems
As far back as the 1920's, algebra had been accepted as the science studying the properties of sets on which there is defined a particular system of operations. However up until the forties the overwhelming majority of algebraists were investigating merel
- PDF / 45,001,037 Bytes
- 331 Pages / 439.32 x 666.12 pts Page_size
- 40 Downloads / 247 Views
Herausgegeben von
J. L. Doob . A. Grothendieck· E. Heinz· F. Hirzebruch E. Hopf . W. Maak . S. MacLane . M. Magnus. J. K. Moser M. M. Postnikov . F. K. Schmidt· D. S. Scott· K. Stein
Geschajtsjiihrende Herausgeber B. Eckmann und B. L. van der Waerden
A. I. Mal'cev
Algebraic Systems Translated from the Russian by B. D. Seckler and A. P. Doohovskoy
With 25 Figures
Springer-Verlag Berlin Heidelberg New York 1973
A. 1. Mal' cev Novosibirsk/USSR
Title of the Russian Original Edition: Algebraiceskie sistemy Edited by D. Smltnov and M. Taiclin Publisher: Izdatelstvo Fiziko-Matematiceskoi literatury, Moscow/USSR 1970
B. D. Seckler
Translators:
Alexander P. Doohovskoy
Great Neck, NY/USA
Concord, MA/USA
Geschaftsfuhrende Herausgeber:
B.Eckmann Eidgenossische Technische Hochschule Zurich
B. L. van der Waerden Mathematisches Institut der Universitat Zurich
An edition of this book is published by the Akademie-Verlag, Berlin, for distribution in socialist countries
AMS Subject Classifications (1970): 02H15, 02J10, 08A05
ISBN-I 3: 978-3-642-65376-6 e-ISBN- I 3: 978-3-642-65374-2 DOl: 10.10°71978-3-642-65374-2 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 similar means, and storage in data banks. Under § 54 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. @) by Springer -Verlag, Berlin. Heidelberg 1973. Softcover reprint of the hardcover 1St edition 1973
Library of Congress Catalog Card Number 72-76761.
From the Editors The author of the book is the eminent Soviet Academician Anatolii Ivanovic Mal'cev whose untimely death occurred July 7, 1967 in his fifty-eight year. The scientific legacy of A. 1. Mal'cev is exceptionally rich and extensive. Many fundamental results in groups, rings, linear algebra, algebraic topology, Lie groups and mathematical logic are due to him. A. 1. Mal'cev was also one of the originators of the theory of algebraic systems. It came into being when the techniques of mathematical logic began to be applied to algebra and so it occupies a position bordering on algebra and logic. Mal'cev published a long series of articles devoted to algebraic systems and delivered several brilliant review talks on the subject at the Third and Fourth All-Union Mathematics Conferences [43J, [45]. In a report to the 1966 International Congress of Mathematicians in Moscow, he set forth a number of new ideas relating to the theory of algebraic systems [48]. Mal'cev began work on the book Algebraic Systems in 1951 during his stay in Ivanov. In 1953, a typewritten copy of the first part was submitted to the Mathematics Department of the Ivanov Pedagogical Institute. Since then, many Soviet algebraists have availed themselves of it. However further work on the book was suspended and
