Noncommutative Rings and Their Applications

280 Pages·2015·1.777 MB·English

by  Steven Dougherty, Alberto Facchini, Andre Leroy, Edmund Puczylowski, Patrick Sole

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.
Sendreq[e-mail].
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