Abstract Algebra An Introductory Course
This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations.
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Gregory T. Lee
Abstract Algebra An Introductory Course
Springer Undergraduate Mathematics Series Advisory Board M.A.J. Chaplain, University of St. Andrews A. MacIntyre, Queen Mary University of London S. Scott, King’s College London N. Snashall, University of Leicester E. Süli, University of Oxford M.R. Tehranchi, University of Cambridge J.F. Toland, University of Bath
More information about this series at http://www.springer.com/series/3423
Gregory T. Lee
Abstract Algebra An Introductory Course
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Gregory T. Lee Department of Mathematical Sciences Lakehead University Thunder Bay, ON Canada
ISSN 1615-2085 ISSN 2197-4144 (electronic) Springer Undergraduate Mathematics Series ISBN 978-3-319-77648-4 ISBN 978-3-319-77649-1 (eBook) https://doi.org/10.1007/978-3-319-77649-1 Library of Congress Control Number: 2018935845 Mathematics Subject Classification (2010): 20-01, 16-01, 12-01 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
In memory of my father
Preface
This book is intended for students encountering the beautiful subject of abstract algebra for the first time. My goal here is to provide a text that is suitable for you, whether you plan to take only a single course in abstract algebra, or to carry on to more advanced courses at the senior undergraduate and graduate levels. Naturally, I wish to encourage you to study the subject further and to ensure that you are prepared if you do so. At many universities, including my own, abstract algebra is the first serious proof-based course taken by mathematics majors. While it is quite possible to get through, let us sa
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