文档介绍：Israel Kleiner
A History of
Abstract Algebra
Birkhauser¨
Boston • Basel • Berlin
Israel Kleiner
Department of Mathematics and Statistics
York University
Toronto, ON M3J 1P3
Canada
kleiner@
Cover design by Alex Gerasev, Revere, MA.
Mathematics Subject Classification (2000): 00-01, 00-02, 01-01, 01-02, 01A55, 01A60, 01A70,
12-03, 13-03, 15-03, 16-03, 20-03, 97-03
Library of Congress Control Number: 2007932362
ISBN-13: 978-0-8176-4684-4 e-ISBN-13: 978-0-8176-4685-1
Printed on acid-free paper.
c 2007 Birkhauser¨ Boston
All rights reserved. This work may not be translated or copied in whole or in part without the writ-
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987654321
(LAP/EB)
With much love to my family
Nava
Ronen, Melissa, Leeor, Tania, Ayelet, Tamir
Tia, Jordana, Jake
Contents
Preface ......................................................... xi
Permissions ..................................................... xv
1 History of Classical Algebra ................................... 1
Early roots ................................................ 1
The Greeks ................................................ 2
Al-Khwarizmi ............................................. 3
Cubic and quartic equations .................................. 5
The cubic plex numbers .............................. 7
Algebraic