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 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 by services 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 general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Acquisitions Department, American Math- ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to [email protected]. Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.) c 2014 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Copyright of individual articles may revert to the public domain 28 years after publication. Contact the AMS for copyright status of individual articles. Printed in the United States of America. ∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ 10987654321 191817161514 Contents 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