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 2527, 2012The Ohio State University, Columbus, OH

Dinh Van HuynhS. K. Jain

Sergio R. Lpez-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 2527, 2012The Ohio State University, Columbus, OH

Dinh Van HuynhS. K. Jain

Sergio R. Lpez-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 2527, 2012The Ohio State University, Columbus, OH

Dinh Van HuynhS. K. Jain

Sergio R. Lpez-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 Classication. 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 2527, 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 2013032319512.44dc23

Contemporary Mathematics ISSN: 0271-4132 (print); ISSN: 1098-3627 (online)

DOI: http://dx.doi.org/10.1090/conm/609

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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 Eggerts ConjectureGeorge M. Bergman 1

p-ExtensionsPapiya Bhattacharjee, Michelle L. Knox,and Warren Wm. McGovern 19

Strongly J-Clean Rings With InvolutionsHuanyin Chen, Abdullah Harmanc, 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 Harmanc 123

Denable Classes and Mittag-Leer 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

Jacobsons 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 2527,2012 in Columbus, Ohio. That installment of the conference served as a commem-oration of Professor Hans Zassenhaus Centennial in 2012, a tting 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 prolic researcher and a magnicent 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 nalversion of the manuscripts you will nd here. We also want to express our deepappreciation to Christine Thivierge and Michael Saitas, who very eciently 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

Mara 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 dArtois

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 Laln, 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 Carf`, Michel L. Lapidus, Erin P. J. Pearse, and Machiel vanFrankenhuijsen, Editors, Fractal Geometry and Dynamical Systems in Pure andApplied Mathematics II, 2013

600 David Carf`, 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 Dierential 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 Dierential Equations II, 2013

594 James B. Serrin, Enzo L. Mitidieri, and Vicentiu D. Radulescu, Editors, RecentTrends in Nonlinear Partial Dierential 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, VladimirMazya, Simeon Reich, David Shoikhet, Gilbert Weinstein, and LawrenceZalcman, Editors, Complex Analysis and Dynamical Systems V, 2013

590 Ursula Hamenstadt, Alan W. Reid, Rub Rodrguez, Steen 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. Lams70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May2527, 2012, at The Ohio State University, Columbus, Ohio.

Included are expository articles and research papers covering topics such as cyclicallypresented modules, Eggerts 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

9 780821 887974

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in,Lpez-Pe

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Preface