609

Ring Theory and Its Applications

Ring Theory Session in Honor of T. Y. Lam on his 70th Birthday 31st Ohio State-Denison Mathematics Conference May 25–27, 2012 The Ohio State University, Columbus, OH

Dinh Van Huynh S. K. Jain Sergio R. López-Permouth S. Tariq Rizvi Cosmin S. Roman Editors

American Mathematical Society Ring Theory and Its Applications

Ring Theory Session in Honor of T. Y. Lam on his 70th Birthday 31st Ohio State-Denison Mathematics Conference May 25–27, 2012 The Ohio State University, Columbus, OH

Dinh Van Huynh S. K. Jain Sergio R. López-Permouth S. Tariq Rizvi Cosmin S. Roman Editors

609

Ring Theory and Its Applications

Ring Theory Session in Honor of T. Y. Lam on his 70th Birthday 31st Ohio State-Denison Mathematics Conference May 25–27, 2012 The Ohio State University, Columbus, OH

Dinh Van Huynh S. K. Jain Sergio R. López-Permouth S. Tariq Rizvi Cosmin S. Roman Editors

American Mathematical Society Providence, 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 70th birthday at the 31st Ohio State-Denison Mathematics Conference, May 25–27, 2012, The Ohio State University, Columbus, OH / Dinh Van Huynh, S. K. Jain, Sergio R. L´opez-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 2013032319 512.44–dc23

Contemporary Mathematics ISSN: 0271-4132 (print); ISSN: 1098-3627 (online) DOI: http://dx.doi.org/10.1090/conm/609

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Preface vii List of Participants ix Thoughts On Eggert’s Conjecture George M. Bergman 1 p-Extensions Papiya Bhattacharjee, Michelle L. Knox, and Warren Wm. McGovern 19 Strongly J-Clean Rings With Involutions Huanyin Chen, Abdullah Harmancı, and A. C¸igdem˘ Ozcan¨ 33 QF Rings Characterized by Injectivities: A Survey Jianlong 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 Factorizations Alberto Facchini, Daniel Smertnig, and Nguyen Khanh Tung 89 Isomorphisms of Some Quantum Spaces Jason Gaddis 107 Additive Unit Representations in Endomorphism Rings and an Extension of a Result of Dickson and Fuller Pedro A. Guil Asensio and Ashish K. Srivastava 117 On a Class of ⊕-Supplemented Modules Burcu Ungor, Sait Halicioglu, and Abdullah Harmancı 123 Definable Classes and Mittag-Leffler Conditions Dolors Herbera 137 A Note on Clean Group Algebras Kanchan Joshi, Pramod Kanwar, and J. B. Srivastava 167 On Dual Baer Modules Derya Keskin Tutunc¨ u,¨ Patrick F. Smith, and Sultan Eylem Toksoy 173 Jacobson’s Lemma for Drazin Inverses T. Y. Lam and Pace P. Nielsen 185

v vi CONTENTS

Transfer of Certain Properties from Modules to their Endomorphism Rings Gangyong Lee, S. Tariq Rizvi, and Cosmin S. Roman 197 From Boolean Rings to Clean Rings Tsiu-Kwen Lee and Yiquiang Zhou 223 On Right Strongly McCoy Rings AndreLeroy´ and Jerzy Matczuk 233 Compatible Ring Structures on Injective Hulls of Finitely Embedded Rings Barbara L. Osofsky 245 Good Matrix Gradings from Directed Graphs Kenneth L. Price and Stephen Szydlik 267 Leavitt Path Algebras Which Are Zorn Rings Kulumani M. Rangaswamy 277 Sheaves That Fail to Represent Matrix Rings Manuel L. Reyes 285 Rings of Invariant Module Type and Automorphism-Invariant Modules Surjeet 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 the conference was initiated by Zassenhaus in the early sixties. At the same time, the Ring 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 volume collects 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 brilliant exposition. He is an inspiring mentor to his PhD students and an excellent role model 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 a tremendous pleasure to do our small part to celebrate his life and accomplishments.

The Ring Theory session of the Ohio State-Denison Mathematics Conference is part of a longstanding tradition of collaboration between the Department of Mathematics of the Ohio State University and the Ohio University Center of Ring Theory and its Applications and has become a mainstay for the worldwide ring theory community. We are thankful to the Mathematics Research institute of The Ohio State University, The Center of Ring Theory and its Applications of Ohio University and The Ohio State University at Lima for their generous support of the conference.

For the most part, contributors to this volume delivered related talks at the conference. All papers were subject to a strict process of refereeing.

We would like to use this opportunity to thank all the anonymous referees who delivered their recommendations about the submissions under a very tight schedule. In many cases, their recommendations and feedback enriched and improved the final version of the manuscripts you will find here. We also want to express our deep appreciation to Christine Thivierge and Michael Saitas, who very efficiently handled this publication on behalf of the American Mathematical Society.

vii

List of Participants

Jawad ABUHLAIL George BERGMAN KFUPM University of California, Berkeley Lulwah AL-ESSA Papiya BHATTACHARJEE Ohio University Penn State Erie, The Behrend College Adel ALAHMADI Gary F. BIRKENMEIER King Abdulaziz University University of Louisiana at Lafayette Mustafa ALKAN Victor BOVDI Akdeniz University University of Debrecen Yousef ALKHAMEES Walter BURGESS King Saud University University of Ottawa Hamed ALSULAMI Victor CAMILLO King Abdulaziz University University of Iowa K.T. ARASU Mikhail CHEBOTAR Wright State University Kent State University Mar´ıa Jos´e ARROYO-PANIAGUA Jianlong CHEN Universidad Autonoma Metropolitana, Southeast University Mexico William CHIN Nuh AYDIN DePaul University Kenyon College Kathi CROW Salem State University Pinar AYDOGDU˘ Hacettepe University Alexander J. DIESL Wellesley College Pradeep BANSAL Indian Institute Of Technology Radoslav DIMITRIC Guwahati CUNY Mamadou BARRY Nanqing DING Cheikh Anta Diop University Dakar Nanjing University Hyman BASS Hai Q. DINH University of Michigan Kent State University Allen D. BELL Thomas J. DORSEY University of Wisconsin-Milwaukee CCR-La Jolla

ix x PARTICIPANTS

Kevin Michael DREES Garrett JOHNSON Edinboro University of Pennsylvania North Carolina State University Nguyen Viet DUNG Martin JURAS Ohio University, Zanesville Qatar University Noyan F. ER Pramod KANWAR University of Rio Grande Ohio University - Zanesville Sergio ESTRADA Sudesh Kaur KHANDUJA Universidad de Murcia Indian Institute of Science Education and Research Alberto FACCHINI University of Padova Dinesh KHURANA Panjab University Mary FLAGG Ekaterina Igorevna KOMPANTSEVA University of Houston Moscow State Pedagogical University Xianhui FU Achlesh KUMARI School of Mathematics and Statistics, S. V. College Northeast Normal University Tai Keun KWAK Jason Dale GADDIS Daejin University University of Wisconsin - Milwaukee T.Y. LAM Kenneth GOODEARL University of California, Berkeley University of California, Santa Barbara Richard Louis LEBLANC Pedro Antonio GUIL-ASENSIO University of Louisiana Lafayette University of Murcia Gangyong LEE Dolors HERBERA The Ohio State University Universitat Autonoma de Barcelona Matthew LENNON Ivo HERZOG University of Louisiana Lafayette The Ohio State University, Lima Andr´eLEROY Christopher HOLSTON Universit´e d’Artois Ohio University Yuanlin LI John S. HSIA Brock University The Ohio State University Qiongling LIU Birge HUISGEN-ZIMMERMANN Southeast University University of California, Santa Barbara Sergio Roberto LOPEZ-PERMOUTH´ Dinh Van HUYNH Ohio University Ohio University Lixin MAO Nanjing Institute of Technology Ursul Mihail ION University of Technology, Lae Joseph MASTROMATTEO Ohio University S.K. JAIN Ohio University and King Abdulaziz Najat Mohammed MATHNI University Ohio University PARTICIPANTS xi

Zachary MESYAN Christopher Edward RYAN University of Colorado, Colorado University of Louisiana at Lafayette Springs Bradford J. SCHLEBEN Ahmad MOJIRI University of Wisconsin - Milwaukee Saint Xavier University Markus SCHMIDMEIER Jeremy Stephen MOORE Florida Atlantic University Otterbein University Ryan SCHWIEBERT Hatice MUTLU Ohio University Izmir Institute of Technology Daniel SHAPIRO W. Keith NICHOLSON The Ohio State University University of Calgary Daniel Richard SHIFFLET Clarion University of Pennsylvania Pace P. NIELSEN Brigham Young University Feroz SIDDIQUE Saint Louis University Gregory Grant OMAN University of Colorado, Colorado Mercedes SILES-MOLINA Springs Universidad de Malaga Hakan OZADAM¨ Jose Eduardo SIMENTAL Ohio University Ohio University Ay¸se C¸i˘gdem OZCAN¨ Tara L. SMITH Hacettepe University University of Cincinnati Nicholas J. PILEWSKI Ashish K. SRIVASTAVA Ohio University St. Louis University ˇ Kenneth PRICE Janez STER University of Wisconsin Oshkosh Institute of Mathematics, Physics and Mechanics, Ljubljana Murtaza Ali QUADRI Nik STOPAR Aligarh Muslim University University of Ljubljana Rekha RANI Pham THUY N. R. E. C. College Moscow State Pedagogical University Manuel Lionel REYES Sultan Eylem TOKSOY Bowdoin College Izmir Institute of Technology Bruce REZNICK Jan TRLIFAJ University of Illinois Univerzita Karlova S. Tariq RIZVI Burcu UNGOR The Ohio State University, Lima Ankara University Cosmin ROMAN Lia VAS The Ohio State University, Lima University of the Sciences Philipp ROTHMALER Nicholas WERNER Graduate Center of CUNY University of Evansville xii PARTICIPANTS

Hasret YAZARLI Ohio University, The Center of Rings and Their Applications Mohamed F. YOUSIF The Ohio State University at Lima Michal ZIEMBOWSKI Warsaw University of Technology Xiaoxiang ZHANG Southeast University Yiqiang ZHOU Memorial University of Newfoundland

Selected Published Titles in This Series

609 Dinh Van Huynh, S. K. Jain, Sergio R. L´opez-Permouth, S. Tariq Rizvi, andCosminS.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, Expository Lectures on Representation Theory, 2014 606 Chantal David, Matilde Lal´ın, and Michelle Manes, Editors, Women in Numbers 2, 2013 605 Omid Amini, Matthew Baker, and Xander Faber, Editors, Tropical and Non-Archimedean Geometry, 2013 604 Jos´eLuisMonta˜na and Luis M. Pardo, Editors, Recent Advances in Real Complexity 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`ı, Michel L. Lapidus, Erin P. J. Pearse, and Machiel van Frankenhuijsen, Editors, Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II, 2013 600 David Carf`ı, Michel L. Lapidus, Erin P. J. Pearse, and Machiel van Frankenhuijsen, Editors, Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I, 2013 599 Mohammad Ghomi, Junfang Li, John McCuan, Vladimir Oliker, Fernando Schwartz, and Gilbert Weinstein, Editors, Geometric Analysis, Mathematical Relativity, 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 Stephan Tillmann, Editors, Geometry and Topology Down Under, 2013 596 Khodr Shamseddine, Editor, Advances in Ultrametric Analysis, 2013 595 James B. Serrin, Enzo L. Mitidieri, and Vicent¸iu D. R˘adulescu, Editors, Recent Trends in Nonlinear Partial Differential Equations II, 2013 594 James B. Serrin, Enzo L. Mitidieri, and Vicent¸iu D. R˘adulescu, Editors, Recent Trends in Nonlinear Partial Differential Equations I, 2013 593 Anton Dzhamay, Kenichi Maruno, and Virgil U. Pierce, Editors, Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, 2013 592 Arkady Berenstein and Vladimir Retakh, Editors, Noncommutative Birational Geometry, Representations and Combinatorics, 2013 591 Mark L. Agranovsky, Matania Ben-Artzi, Greg Galloway, Lavi Karp, Vladimir Maz’ya, Simeon Reich, David Shoikhet, Gilbert Weinstein, and Lawrence Zalcman, Editors, Complex Analysis and Dynamical Systems V, 2013 590 Ursula Hamenst¨adt, Alan W. Reid, Rub´ıRodr´ıguez, Steffen Rohde, and Michael Wolf, Editors, In the Tradition of Ahlfors-Bers, VI, 2013 589 Erwan Brugall´e, Mari´aAng´elica Cueto, Alicia Dickenstein, Eva-Maria Feichtner, and Ilia Itenberg, Editors, Algebraic and Combinatorial Aspects of Tropical 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 the AMS Bookstore at www.ams.org/bookstore/conmseries/. CONM 609 igTheory Ring • un,Ji,LpzProt,Rzi Roman Rizvi, López-Permouth, Jain, Huynh, This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam’s 70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May 25–27, 2012, at The Ohio State University, Columbus, Ohio. Included are expository articles and research papers covering topics such as cyclically presented modules, Eggert’s conjecture, the Mittag-Leffler conditions, clean rings, McCoy rings, 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 articles contain explicit lists of open questions.

ISBN 978-0-8218-8797-4

9 780821 887974

CONM/609 AMS