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609
Ring Theory and Its Applications
Ring Theory Session in Honor of T. Y. Lam on his 70th Birthday31st Ohio State-Denison Mathematics Conference
May 25–27, 2012The Ohio State University, Columbus, OH
Dinh Van HuynhS. K. Jain
Sergio R. López-PermouthS. Tariq Rizvi
Cosmin S. RomanEditors
American Mathematical Society
Ring Theory and Its Applications
Ring Theory Session in Honor of T. Y. Lam on his 70th Birthday31st Ohio State-Denison Mathematics Conference
May 25–27, 2012The Ohio State University, Columbus, OH
Dinh Van HuynhS. K. Jain
Sergio R. López-PermouthS. Tariq Rizvi
Cosmin S. RomanEditors
609
Ring Theory and Its Applications
Ring Theory Session in Honor of T. Y. Lam on his 70th Birthday31st Ohio State-Denison Mathematics Conference
May 25–27, 2012The Ohio State University, Columbus, OH
Dinh Van HuynhS. K. Jain
Sergio R. López-PermouthS. Tariq Rizvi
Cosmin S. RomanEditors
American Mathematical SocietyProvidence, Rhode Island
EDITORIAL COMMITTEE
Dennis DeTurck, Managing Editor
Michael Loss Kailash Misra Martin J. Strauss
2010 Mathematics Subject Classification. Primary 16-XX, 13A25, 13C10, 13E10, 14A22,18B25, 18F20, 20G07.
Library of Congress Cataloging-in-Publication Data
Ring Theory Session (2012 : Columbus, Ohio)Ring theory and its applications : Ring Theory Session in honor of T. Y. Lam on his 70thbirthday at the 31st Ohio State-Denison Mathematics Conference, May 25–27, 2012, The OhioState University, Columbus, OH / Dinh Van Huynh, S. K. Jain, Sergio R. Lopez-Permouth,S. Tariq Rizvi, Cosmin S. Roman, editors.
pages cm. – (Contemporary mathematics ; volume 609)Includes bibliographical references.ISBN 978-0-8218-8797-4 (alk. paper)1. Rings (Algebra)–Congresses. I. Lam, T. Y. (Tsit-Yuen), 1942– honouree. II. Huynh,
Dinh Van, 1947– editor of compilation. III. Ohio State-Denison Mathematics Conference (2012 :Columbus, Ohio) IV. Title.QA247.R57516 2012 2013032319512′.44–dc23
Contemporary Mathematics ISSN: 0271-4132 (print); ISSN: 1098-3627 (online)
DOI: http://dx.doi.org/10.1090/conm/609
Copying and reprinting. Material in this book may be reproduced by any means for edu-cational and scientific purposes without fee or permission with the exception of reproduction byservices that collect fees for delivery of documents and provided that the customary acknowledg-ment of the source is given. This consent does not extend to other kinds of copying for generaldistribution, for advertising or promotional purposes, or for resale. Requests for permission forcommercial use of material should be addressed to the Acquisitions Department, American Math-ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests canalso be made by e-mail to reprint-permission@ams.org.
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10 9 8 7 6 5 4 3 2 1 19 18 17 16 15 14
Contents
Preface vii
List of Participants ix
Thoughts On Eggert’s ConjectureGeorge M. Bergman 1
p-ExtensionsPapiya Bhattacharjee, Michelle L. Knox,
and Warren Wm. McGovern 19
Strongly J-Clean Rings With InvolutionsHuanyin Chen, Abdullah Harmancı, and A. Cigdem Ozcan 33
QF Rings Characterized by Injectivities: A SurveyJianlong Chen, Wenxi Li, and Liang Shen 45
Repeated-Root Cyclic and Negacyclic Codes of Length 6ps
Hai Q. Dinh 69
Cyclically Presented Modules, Projective Covers and FactorizationsAlberto Facchini, Daniel Smertnig, and Nguyen Khanh Tung 89
Isomorphisms of Some Quantum SpacesJason Gaddis 107
Additive Unit Representations in Endomorphism Rings and an Extension of aResult of Dickson and Fuller
Pedro A. Guil Asensio and Ashish K. Srivastava 117
On a Class of ⊕-Supplemented ModulesBurcu Ungor, Sait Halicioglu, and Abdullah Harmancı 123
Definable Classes and Mittag-Leffler ConditionsDolors Herbera 137
A Note on Clean Group AlgebrasKanchan Joshi, Pramod Kanwar, and J. B. Srivastava 167
On Dual Baer ModulesDerya Keskin Tutuncu, Patrick F. Smith,
and Sultan Eylem Toksoy 173
Jacobson’s Lemma for Drazin InversesT. Y. Lam and Pace P. Nielsen 185
v
vi CONTENTS
Transfer of Certain Properties from Modules to their Endomorphism RingsGangyong Lee, S. Tariq Rizvi, and Cosmin S. Roman 197
From Boolean Rings to Clean RingsTsiu-Kwen Lee and Yiquiang Zhou 223
On Right Strongly McCoy RingsAndre Leroy and Jerzy Matczuk 233
Compatible Ring Structures on Injective Hulls of Finitely Embedded RingsBarbara L. Osofsky 245
Good Matrix Gradings from Directed GraphsKenneth L. Price and Stephen Szydlik 267
Leavitt Path Algebras Which Are Zorn RingsKulumani M. Rangaswamy 277
Sheaves That Fail to Represent Matrix RingsManuel L. Reyes 285
Rings of Invariant Module Type and Automorphism-Invariant ModulesSurjeet Singh and Ashish K. Srivastava 299
Preface
The 31st Ohio State-Denison Mathematics Conference was held May 25–27,2012 in Columbus, Ohio. That installment of the conference served as a commem-oration of Professor Hans Zassenhaus’ Centennial in 2012, a fitting tribute as theconference was initiated by Zassenhaus in the early sixties. At the same time, theRing Theory Session of that conference was dedicated to a celebration of Univer-sity of California-Berkeley Professor T.Y. Lam on his 70th Birthday. This volumecollects the proceedings of the Ring Theory session and, just like the session itself,is dedicated to Professor Lam.
T.Y. Lam is a prolific researcher and a magnificent writer. His books are trea-sured by students and researchers alike because of their thoroughness and brilliantexposition. He is an inspiring mentor to his PhD students and an excellent rolemodel to his post-doctoral visitors. We consider ourselves lucky to have a profes-sional relationship with him and are honored to count him as a friend. It has been atremendous pleasure to do our small part to celebrate his life and accomplishments.
The Ring Theory session of the Ohio State-Denison Mathematics Conferenceis part of a longstanding tradition of collaboration between the Department ofMathematics of the Ohio State University and the Ohio University Center of RingTheory and its Applications and has become a mainstay for the worldwide ringtheory community. We are thankful to the Mathematics Research institute of TheOhio State University, The Center of Ring Theory and its Applications of OhioUniversity and The Ohio State University at Lima for their generous support ofthe conference.
For the most part, contributors to this volume delivered related talks at theconference. All papers were subject to a strict process of refereeing.
We would like to use this opportunity to thank all the anonymous referees whodelivered their recommendations about the submissions under a very tight schedule.In many cases, their recommendations and feedback enriched and improved the finalversion of the manuscripts you will find here. We also want to express our deepappreciation to Christine Thivierge and Michael Saitas, who very efficiently handledthis publication on behalf of the American Mathematical Society.
vii
List of Participants
Jawad ABUHLAILKFUPM
Lulwah AL-ESSAOhio University
Adel ALAHMADIKing Abdulaziz University
Mustafa ALKANAkdeniz University
Yousef ALKHAMEESKing Saud University
Hamed ALSULAMIKing Abdulaziz University
K.T. ARASUWright State University
Marıa Jose ARROYO-PANIAGUAUniversidad Autonoma Metropolitana,Mexico
Nuh AYDINKenyon College
Pinar AYDOGDUHacettepe University
Pradeep BANSALIndian Institute Of TechnologyGuwahati
Mamadou BARRYCheikh Anta Diop University Dakar
Hyman BASSUniversity of Michigan
Allen D. BELLUniversity of Wisconsin-Milwaukee
George BERGMANUniversity of California, Berkeley
Papiya BHATTACHARJEEPenn State Erie, The Behrend College
Gary F. BIRKENMEIERUniversity of Louisiana at Lafayette
Victor BOVDIUniversity of Debrecen
Walter BURGESSUniversity of Ottawa
Victor CAMILLOUniversity of Iowa
Mikhail CHEBOTARKent State University
Jianlong CHENSoutheast University
William CHINDePaul University
Kathi CROWSalem State University
Alexander J. DIESLWellesley College
Radoslav DIMITRICCUNY
Nanqing DINGNanjing University
Hai Q. DINHKent State University
Thomas J. DORSEYCCR-La Jolla
ix
x PARTICIPANTS
Kevin Michael DREESEdinboro University of Pennsylvania
Nguyen Viet DUNGOhio University, Zanesville
Noyan F. ERUniversity of Rio Grande
Sergio ESTRADAUniversidad de Murcia
Alberto FACCHINIUniversity of Padova
Mary FLAGGUniversity of Houston
Xianhui FUSchool of Mathematics and Statistics,Northeast Normal University
Jason Dale GADDISUniversity of Wisconsin - Milwaukee
Kenneth GOODEARLUniversity of California, Santa Barbara
Pedro Antonio GUIL-ASENSIOUniversity of Murcia
Dolors HERBERAUniversitat Autonoma de Barcelona
Ivo HERZOGThe Ohio State University, Lima
Christopher HOLSTONOhio University
John S. HSIAThe Ohio State University
Birge HUISGEN-ZIMMERMANNUniversity of California, Santa Barbara
Dinh Van HUYNHOhio University
Ursul Mihail IONUniversity of Technology, Lae
S.K. JAINOhio University and King AbdulazizUniversity
Garrett JOHNSONNorth Carolina State University
Martin JURASQatar University
Pramod KANWAROhio University - Zanesville
Sudesh Kaur KHANDUJAIndian Institute of Science Educationand Research
Dinesh KHURANAPanjab University
Ekaterina Igorevna KOMPANTSEVAMoscow State Pedagogical University
Achlesh KUMARIS. V. College
Tai Keun KWAKDaejin University
T.Y. LAMUniversity of California, Berkeley
Richard Louis LEBLANCUniversity of Louisiana Lafayette
Gangyong LEEThe Ohio State University
Matthew LENNONUniversity of Louisiana Lafayette
Andre LEROYUniversite d’Artois
Yuanlin LIBrock University
Qiongling LIUSoutheast University
Sergio Roberto LOPEZ-PERMOUTHOhio University
Lixin MAONanjing Institute of Technology
Joseph MASTROMATTEOOhio University
Najat Mohammed MATHNIOhio University
PARTICIPANTS xi
Zachary MESYANUniversity of Colorado, ColoradoSprings
Ahmad MOJIRISaint Xavier University
Jeremy Stephen MOOREOtterbein University
Hatice MUTLUIzmir Institute of Technology
W. Keith NICHOLSONUniversity of Calgary
Pace P. NIELSENBrigham Young University
Gregory Grant OMANUniversity of Colorado, ColoradoSprings
Hakan OZADAMOhio University
Ayse Cigdem OZCANHacettepe University
Nicholas J. PILEWSKIOhio University
Kenneth PRICEUniversity of Wisconsin Oshkosh
Murtaza Ali QUADRIAligarh Muslim University
Rekha RANIN. R. E. C. College
Manuel Lionel REYESBowdoin College
Bruce REZNICKUniversity of Illinois
S. Tariq RIZVIThe Ohio State University, Lima
Cosmin ROMANThe Ohio State University, Lima
Philipp ROTHMALERGraduate Center of CUNY
Christopher Edward RYANUniversity of Louisiana at Lafayette
Bradford J. SCHLEBENUniversity of Wisconsin - Milwaukee
Markus SCHMIDMEIERFlorida Atlantic University
Ryan SCHWIEBERTOhio University
Daniel SHAPIROThe Ohio State University
Daniel Richard SHIFFLETClarion University of Pennsylvania
Feroz SIDDIQUESaint Louis University
Mercedes SILES-MOLINAUniversidad de Malaga
Jose Eduardo SIMENTALOhio University
Tara L. SMITHUniversity of Cincinnati
Ashish K. SRIVASTAVASt. Louis University
Janez STERInstitute of Mathematics, Physics andMechanics, Ljubljana
Nik STOPARUniversity of Ljubljana
Pham THUYMoscow State Pedagogical University
Sultan Eylem TOKSOYIzmir Institute of Technology
Jan TRLIFAJUniverzita Karlova
Burcu UNGORAnkara University
Lia VASUniversity of the Sciences
Nicholas WERNERUniversity of Evansville
xii PARTICIPANTS
Hasret YAZARLIOhio University, The Center of Ringsand Their Applications
Mohamed F. YOUSIFThe Ohio State University at Lima
Michal ZIEMBOWSKIWarsaw University of Technology
Xiaoxiang ZHANGSoutheast University
Yiqiang ZHOUMemorial University of Newfoundland
Selected Published Titles in This Series
609 Dinh Van Huynh, S. K. Jain, Sergio R. Lopez-Permouth, S. Tariq Rizvi,and Cosmin S. Roman, Editors, Ring Theory and Its Applications, 2014
608 Robert S. Doran, Greg Friedman, and Scott Nollet, Editors, Hodge Theory,Complex Geometry, and Representation Theory, 2014
607 Kiyoshi Igusa, Alex Martsinkovsky, and Gordan Todorov, Editors, ExpositoryLectures on Representation Theory, 2014
606 Chantal David, Matilde Lalın, and Michelle Manes, Editors, Women in Numbers2, 2013
605 Omid Amini, Matthew Baker, and Xander Faber, Editors, Tropical andNon-Archimedean Geometry, 2013
604 Jose Luis Montana and Luis M. Pardo, Editors, Recent Advances in RealComplexity and Computation, 2013
603 Azita Mayeli, Alex Iosevich, Palle E. T. Jorgensen, and Gestur Olafsson,Editors, Commutative and Noncommutative Harmonic Analysis and Applications, 2013
602 Vyjayanthi Chari, Jacob Greenstein, Kailash C. Misra, K. N. Raghavan,and Sankaran Viswanath, Editors, Recent Developments in Algebraic and
Combinatorial Aspects of Representation Theory, 2013
601 David Carfı, Michel L. Lapidus, Erin P. J. Pearse, and Machiel vanFrankenhuijsen, Editors, Fractal Geometry and Dynamical Systems in Pure andApplied Mathematics II, 2013
600 David Carfı, Michel L. Lapidus, Erin P. J. Pearse, and Machiel vanFrankenhuijsen, Editors, Fractal Geometry and Dynamical Systems in Pure andApplied Mathematics I, 2013
599 Mohammad Ghomi, Junfang Li, John McCuan, Vladimir Oliker, Fernando
Schwartz, and Gilbert Weinstein, Editors, Geometric Analysis, MathematicalRelativity, and Nonlinear Partial Differential Equations, 2013
598 Eric Todd Quinto, Fulton Gonzalez, and Jens Gerlach Christensen, Editors,Geometric Analysis and Integral Geometry, 2013
597 Craig D. Hodgson, William H. Jaco, Martin G. Scharlemann, and StephanTillmann, Editors, Geometry and Topology Down Under, 2013
596 Khodr Shamseddine, Editor, Advances in Ultrametric Analysis, 2013
595 James B. Serrin, Enzo L. Mitidieri, and Vicentiu D. Radulescu, Editors, RecentTrends in Nonlinear Partial Differential Equations II, 2013
594 James B. Serrin, Enzo L. Mitidieri, and Vicentiu D. Radulescu, Editors, RecentTrends in Nonlinear Partial Differential Equations I, 2013
593 Anton Dzhamay, Kenichi Maruno, and Virgil U. Pierce, Editors, Algebraic andGeometric Aspects of Integrable Systems and Random Matrices, 2013
592 Arkady Berenstein and Vladimir Retakh, Editors, Noncommutative BirationalGeometry, Representations and Combinatorics, 2013
591 Mark L. Agranovsky, Matania Ben-Artzi, Greg Galloway, Lavi Karp, VladimirMaz’ya, Simeon Reich, David Shoikhet, Gilbert Weinstein, and LawrenceZalcman, Editors, Complex Analysis and Dynamical Systems V, 2013
590 Ursula Hamenstadt, Alan W. Reid, Rubı Rodrıguez, Steffen Rohde,and Michael Wolf, Editors, In the Tradition of Ahlfors-Bers, VI, 2013
589 Erwan Brugalle, Maria Angelica Cueto, Alicia Dickenstein, Eva-Maria
Feichtner, and Ilia Itenberg, Editors, Algebraic and Combinatorial Aspects ofTropical Geometry, 2013
588 David A. Bader, Henning Meyerhenke, Peter Sanders, and Dorothea Wagner,Editors, Graph Partitioning and Graph Clustering, 2013
For a complete list of titles in this series, visit theAMS Bookstore at www.ams.org/bookstore/conmseries/.
This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam’s70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May25–27, 2012, at The Ohio State University, Columbus, Ohio.
Included are expository articles and research papers covering topics such as cyclicallypresented modules, Eggert’s conjecture, the Mittag-Leffler conditions, clean rings, McCoyrings, QF rings, projective and injective modules, Baer modules, and Leavitt path algebras.
Graduate students and researchers in many areas of algebra will find this volume valu-able as the papers point out many directions for future work; in particular, several articlescontain explicit lists of open questions.
ISBN978-0-8218-8797-4
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CONM/609
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Huynh,Ja
in,Lóp
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