Semilocal Categories and Modules with Semilocal Endomorphism Rings
This book collects and coherently presents the research that has been undertaken since the author’s previous book Module Theory (1998). In addition to some of the key results since 1995, it also discusses the development of much of the supp
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Alberto Facchini
Semilocal Categories and Modules with Semilocal Endomorphism Rings
Progress in Mathematics Volume 331
Series Editors Antoine Chambert-Loir, Université Paris-Diderot, Paris, France Jiang-Hua Lu, The University of Hong Kong, Hong Kong SAR, China Michael Ruzhansky, Imperial College, London, UK Yuri Tschinkel, Courant Institute of Mathematical Sciences, New York, USA
More information about this series at http://www.springer.com/series/4848
Alberto Facchini
Semilocal Categories and Modules with Semilocal Endomorphism Rings
Alberto Facchini Department of Mathematics “Tullio Levi-Civita” University of Padova Padova, Italy
ISSN 2296-505X (electronic) ISSN 0743-1643 Progress in Mathematics ISBN 978-3-030-23283-2 ISBN 978-3-030-23284-9 (eBook) https://doi.org/10.1007/978-3-030-23284-9 Mathematics Subject Classification (2010): 16D70, 16L30, 16S50, 18E05, 18E15, 20M14 © Springer Nature Switzerland AG 2019 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. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
This book is dedicated to Gena Puninski Exegi monumentum aere perennius regalique situ pyramidum altius, quod non imber edax, non Aquilo inpotens possit diruere aut innumerabilis annorum series et fuga temporum. Non omnis moriar. . . (Horace, Odes, III, 30, 1–6)
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xv
1 Monoids, Krull Monoids, Large Monoids 1.1 Commutative Monoids . . . . . . . . . . . . . . . . . . 1.2 Preordered Groups, Positive Cones . . . . . . . . . . . 1.3 The Monoid V (C), Discrete Valuations, Krull Monoids 1.4 Essential Morphis
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