Module Theory, Extending Modules and Generalizations
The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modu
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Adnan Tercan Canan C. Yücel
Module Theory, Extending Modules and
Generalizations
Frontiers in Mathematics
Advisory Editorial Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta) William Y. C. Chen (Nankai University, Tianjin, China) Benoît Perthame (Université Pierre et Marie Curie, Paris) Laurent Saloff-Coste (Cornell University, Ithaca) Igor Shparlinski (Macquarie University, New South Wales) Wolfgang Sprössig (TU Bergakademie Freiberg) Cédric Villani (Institut Henri Poincaré, Paris)
More information about this series at http://www.springer.com/series/5388
Adnan Tercan • Canan C. Yücel
Module Theory, Extending Modules and Generalizations With the cooperation of Patrick F. Smith, University of Glasgow
Adnan Tercan Department of Mathematics Hacettepe University Ankara, Turkey
Canan C. Yücel Department of Mathematics Pamukkale University Denizli, Turkey
ISSN 1660-8046 ISSN 1660-8054 (electronic) Frontiers in Mathematics ISBN 978-3-0348-0950-4 ISBN 978-3-0348-0952-8 (eBook) DOI 10.1007/978-3-0348-0952-8 Library of Congress Control Number: 2016940427 Mathematics Subject Classification (2010): 16D10, 16D40, 16D50, 16D70, 16L30, 16L60, 16P20, 16P60, 16S50, 16S90 © Springer International Publishing Switzerland 2016 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. Printed on acid-free paper This book is published under the trade name Birkhäuser. The registered company is Springer International Publishing AG (www.birkhauser-science.com)
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii A Partial List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix 1 Introducing Modules 1.1 Modules . . . . . . . . Exercises . . . . . . . . . . 1.2 Homomorphisms . . . Exercises . . . . . . . . . . 1.3 Submodules . . . . . . Exercises . . . . . . . . . . 1.4 Projecti
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