Advances in Rings, Modules and Factorizations Graz, Austria, Februar

Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, in

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Alberto Facchini Marco Fontana Alfred Geroldinger Bruce Olberding   Editors

Advances in Rings, Modules and Factorizations Graz, Austria, February 19–23, 2018

Springer Proceedings in Mathematics & Statistics Volume 321

Springer Proceedings in Mathematics & Statistics This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including operation research and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today.

More information about this series at http://www.springer.com/series/10533

Alberto Facchini Marco Fontana Alfred Geroldinger Bruce Olberding •





Editors

Advances in Rings, Modules and Factorizations Graz, Austria, February 19–23, 2018

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Editors Alberto Facchini Dipartimento di Matematica “Tullio Levi-Civita” Università degli Studi di Padova Padua, Italy Alfred Geroldinger Institut für Mathematik und Wissenschaftliches Rechnen Universität Graz Graz, Austria

Marco Fontana Dipartimento di Matematica e Fisica Università degli Studi Roma Tre Rome, Italy Bruce Olberding Department of Mathematical Sciences New Mexico State University Las Cruces, NM, USA

ISSN 2194-1009 ISSN 2194-1017 (electronic) Springer Proceedings in Mathematics & Statistics ISBN 978-3-030-43415-1 ISBN 978-3-030-43416-8 (eBook) https://doi.org/10.1007/978-3-030-43416-8 Mathematics Subject Classification (2010): 13A15, 13A50, 13B21, 13F15, 13G05, 13H99, 14H99, 16D25, 20M25 © Springer Nature Switzerland AG 2020 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 jurisdictiona