Noncommutative Rings and Their Applications PDF
Preview Noncommutative Rings and Their Applications
634 Noncommutative Rings and Their Applications International Conference on Noncommutative Rings and Their Applications July 1–4, 2013 Université d’Artois, Lens, France Steven Dougherty Alberto Facchini André Leroy Edmund Puczyłowski Patrick Solé Editors AmericanMathematicalSociety Noncommutative Rings and Their Applications International Conference on Noncommutative Rings and Their Applications July 1–4, 2013 Université d’Artois, Lens, France Steven Dougherty Alberto Facchini André Leroy Edmund Puczyłowski Patrick Solé Editors 634 Noncommutative Rings and Their Applications International Conference on Noncommutative Rings and Their Applications July 1–4, 2013 Université d’Artois, Lens, France Steven Dougherty Alberto Facchini André Leroy Edmund Puczyłowski Patrick Solé Editors AmericanMathematicalSociety Providence,RhodeIsland Editorial Board of Contemporary Mathematics Dennis DeTurck, managing editor Michael Loss Kailash Misra Martin J. Strauss 2010 Mathematics Subject Classification. Primary 16N60, 16P60, 16S34, 16S99, 16U99, 17B35, 94B05, 94B15, 94B60. Library of Congress Cataloging-in-Publication Data InternationalConferenceonNoncommutativeRingsandTheirApplications (2013: Artois,France) Noncommutative rings and their applications : International Conference on Noncommutative Rings and Their Applications, July 1–4, 2013, University of Artois, France / Steven Dougherty, AlbertoFacchini,Andr´eLeroy,EdmundPuczy(cid:2)lowski,PatrickSol´e,editors. pagescm. –(Contemporarymathematics;volume634) Includesbibliographicalreferences. ISBN978-1-4704-1032-2(alk. paper) 1. Noncommutative rings–Congresses. 2. Rings (Algebra)–Congresses. I. Dougherty, Steven, 1966–editor. II.Facchini,Alberto,editor. III.Leroy,Andr´e(Andr´eGerard),1955–editor. IV.Puczy(cid:2)lowski,Edmund,editor. V.Sol´e,Patrick,1960–editor. VI.Title. QA251.4.I582014 512(cid:2).46–dc23 2014029564 ContemporaryMathematicsISSN:0271-4132(print);ISSN:1098-3627(online) DOI:http://dx.doi.org/10.1090/conm/634 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for useinteachingorresearch. Permissionisgrantedtoquotebriefpassagesfromthispublicationin reviews,providedthecustomaryacknowledgmentofthesourceisgiven. Republication,systematiccopying,ormultiplereproductionofanymaterialinthispublication is permitted only under license from the American Mathematical Society. Permissions to reuse portions of AMS publication content are handled by Copyright Clearance Center’s RightsLink(cid:2) service. Formoreinformation,pleasevisit: http://www.ams.org/rightslink. Sendrequestsfortranslationrightsandlicensedreprintstoreprint-permission@ams.org. Excludedfromtheseprovisionsismaterialforwhichtheauthorholdscopyright. Insuchcases, requestsforpermissiontoreuseorreprintmaterialshouldbeaddresseddirectlytotheauthor(s). Copyrightownershipisindicatedonthecopyrightpage,oronthelowerright-handcornerofthe firstpageofeacharticlewithinproceedingsvolumes. (cid:2)c 2015bytheAmericanMathematicalSociety. Allrightsreserved. TheAmericanMathematicalSocietyretainsallrights exceptthosegrantedtotheUnitedStatesGovernment. Copyrightofindividualarticlesmayreverttothepublicdomain28years afterpublication. ContacttheAMSforcopyrightstatusofindividualarticles. PrintedintheUnitedStatesofAmerica. (cid:2)∞ Thepaperusedinthisbookisacid-freeandfallswithintheguidelines establishedtoensurepermanenceanddurability. VisittheAMShomepageathttp://www.ams.org/ 10987654321 201918171615 Contents Preface vii List of Participants ix Leavitt Path Algebras of Cayley Graphs Arising from Cyclic Groups Gene Abrams and Benjamin Schoonmaker 1 Characterizations of Almost Injective Modules Adel Alahmadi, S. K. Jain, and Surjeet Singh 11 Automorphism-Invariant Modules Pedro A. Guil Asensio and Ashish K. Srivastava 19 Distributive Algebras, Isoclinism, and Invariant Probabilities Stephen M. Buckley 31 Ideals of the Enveloping Algebra U(sl ) 3 Stefan Catoiu 53 On Second Submodules Sec¸il C¸eken and Mustafa Alkan 67 Open Problems in Coding Theory Steven T. Dougherty, Jon-Lark Kim, and Patrick Sol´e 79 Foundations of Algebraic Coding Theory Steven T. Dougherty 101 Counting Z Z -Additive Codes 2 4 Steven T. Dougherty and Esengu¨l Saltu¨rk 137 From Endomorphism Rings to Some Noteworthy Ideals in Categories of Modules Alberto Facchini 149 Lie and Jordan Properties in Group Algebras Edgar G. Goodaire and C´esar Polcino Milies 163 Rad-Projective δ Covers Yasser Ibrahim and Mohamed Yousif 175 On Lattices of Annihilators Ma(cid:2)lgorzata Jastrze¸bska and Jan Krempa 189 v vi CONTENTS Clean Elements in Polynomial Rings Pramod Kanwar, Andr´e Leroy, and Jerzy Matczuk 197 On the Semiprime Smash Product Question Christian Lomp 205 Minimal Prime Ideals and Derivations Jerzy Matczuk 223 On Codes over Local Frobenius Non-Chain Rings of Order 16 Edgar Mart´ınez-Moro and Steve Szabo 227 On Quasi-Duo Rings E. R. Puczyl(cid:2)owski 243 Isomorphism Invariants of Enveloping Algebras Hamid Usefi 253 Preface TheaimoftheInternationalConferenceonNonncommutativeRingsandTheir Applications, held in Lens, France, in July 2013 was to gather specialists in ring theory and in areas where this theory is used. The meeting gave the experts from different domains the opportunity to exchange their views, share their research, and learn from one another new results and problems in a friendly atmosphere. The works of the conference concerned, on one hand, classical aspects of ring and module theory and, on the other, some applications of this theory, focusing on coding theory, in which rings and modules play a more and more substantial role. The interplay betweenring and codingtheory was emphasized by Professor Steven Dougherty’s course in which he showed some of the ways (noncommutative) ring theory has influenced coding theory. The four invited speakers, Alberto Facchini, DolorsHerbera,EdmundPuczy(cid:3)lowski,andPatrickSol´e,presentedtheirmostrecent works and many participants contributed to enrich further the themes addressed by this conference. This meeting was supported by the Laboratoire de Math´ematiques de Lens (LML), by different bodies from the Universit´e de Artois (RI, BQR), as well as by a regional organization (the F´ed´eration des Laboratoires de Math´ematiques du Nord pas de Calais). We would like to thank all the participants for their efforts and enthusiasm. Special thanks to Pramod Kanwar and Jerzy Matczuk who, during the conference, made practical matters go more smoothly. A very special thanks to the colleagues who kindly agreed to referee the pa- pers. Their expertise, promptitude, and professionalism improved the quality of the articles in this volume. Many thanks are due to the editorial staff of the AMS, in particular Christine Thivierge, for the very efficient way she managed the process of preparing and publishing these proceedings. The Editors vii List of Participants Gene Abrams Cristina Fernandez-Cordoba University of Colorado Universitat Aut`onoma de Barcelona Mustafa Alkan Walter Ferrer Akdeniz University Antalya Universidad de la Repu´blica, Montevideo Mamadou Barry Universit´e Cheikh Anta Diop Dakar Yuval Ginosar Haifa University Vladimir Bavula Sheffield University Fatmanur Gursoy Mai Hoang Bien Yildiz Technical University, Istanbul Leiden University Dolors Herbera Geoffrey Booth Universitat Aut`onoma de Barcelona N. Mandela Metropolitan University Ma(cid:3)lgorzata Hryniewicka Port Elizabeth Bia(cid:3)lystok University M’Hammed Boulagouaz Facult´e des Sciences et Techniques, F`es, Dijana Jakelic Morocco University of North Carolina, Wilmington and Stephen Buckley Max Planck Institute for Mathematics, National University of Ireland Bonn Maynooth David Jordan Marion Candau Sheffield University Universit´e de Bretagne Occidentale Brest Pramod Kanwar Ohio University Stefan Catoiu De Paul University, Chicago Suat Karadeniz Fatih University, Istanbul Ahmed Cherchem Universit´e USTHB, Alger Vladislav Kharchenko Nadeem Ahmed Dar National Autonomous University of Mexico (UNAM) Aligarh Muslim University Steven Dougherty Jan Krempa Scranton University Warsaw University Alberto Facchini Andr´e Leroy Padova University Universit´e d’Artois, Lens ix
The list of books you might like
