Abelian Groups and Modules

Mathematics and Its Applications

Managing Editor:

M. HAZEWINKEL

Centre for Mathematics and Computer Science, Amsterdam, The Netherlands

Volume 343

Abelian Groups and Modules Proceedings of the Padova Conference, Padova, Italy, June 23-July 1, 1994

edited by

Alberto Facchini Department of Maţhematics and Infonnatics, University of Udille, Udine, Italy

and

Claudia Menini Department of Mathematics, University of Ferrara, Ferrara,ltaly

.... " SPRINGER SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-94-010-4198-0 ISBN 978-94-011-0443-2 (eBook) DOI 10.1007/978-94-011-0443-2

Printed on acid-free paper

AU Rights Reserved © 1995 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1995 Softcover reprint ofthe hardcover lst edition 1995 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

Dedicated to Laszlo Fuchs on his 70th birthday

TABLE OF CONTENTS

Preface Acknowledgements Conference Information

T. Albu and P.F. Smith Dual relative Krull dimension of modules over commutative rings.

P. N. Anh

xi xiii xv

1

Morita duality, linear compactness and AB5*: a survey . . . . . . 17

D. M. Arnold Near isomorphism of Butler groups and representations of finite posets . 29

D. M. Arnold and M. Dugas Locally free finite rank Butler groups and near isomorphism . . . . . . . .. 41

L. Bican Subgroups of Butler groups. . . . . 49

A. Blass, J. Irwin and G. Schlitt Some abelian groups with free duals . . . . . . . . . . . . . . . . . . . . 57

W. D. Burgess Confirmation of a conjecture of Dauns and Hofmann on biregular rings 67

S. Caenepeel and e. Raianu Induction functors for the Doi-Koppinen unified Hopf modules

N. Cimen, R. Wiegand and S. Wiegand One-dimensional rings of finite representation type

D. Dikranjan Uniqueness of dualities . . . . . . . . . . . . . . . .

P. C. Eklof Classification and non-classification results for abelian groups .

A. Facchini and G. Puninski 'E-pure-injective modules over serial rings. . . . . . . .

T. G. Faticoni Modules over endomorphism rings as homotopy classes

A. Fomin and W. J. Wickless Categories of mixed and torsion-free finite rank abelian groups

K. R. Fuller Reflexive representations of algebras. . . . . . .

R. Gilmer Zero-dimensional subrings of commutative rings . . . . . . . . .

F. Girolami and S. E. Kabbaj The dimension of the tensor product of two particular pullbacks .

73

95

123

135

145

163

185

193

209

221

viii TABLE OF CONTENTS

R. Gobel and S. Shelah On the existence of rigid Nl -free abelian groups of cardinality Nl 227

H. P. Goeters Warfield duality and module extensions over a noetherian domain 239

K. R. Goodearl Von Neumann regular rings and direct sum decomposition problems 249

D. Happel Selforthogonal modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

w. J. Heinzer Subrings of finite-dimensional rings . . . . . . . . . . . . . . . . . . . .. 277

P. Hill and C. Megibben Primary abelian groups whose countable subgroups have countable closure 283

P. Hill and W. Ullery Isotype separable subgroups of totally projective groups. . . . . . . . . . . . 291

P. Keef Representable preradicals with enough projectives .

J. Krempa Rings with periodic unit groups . . . . . . . . . .

F. V. Kuhlmann Abelian groups with contractions II: Weak o-minimality

A. Mader Almost completely decomposable torsion-free abelian groups

S. Mohamed and B. J. Muller On the exchange property for quasi-continuous modules

o. Mutzbauer Endomorphism rings of Reid groups. . . . . . . . . . .

L. G. Nongxa and C. Vinsonhaler Completely decomposable subgroups and factors of finite rank completely

301

313

323

343

367

373

decomposable groups . . . . . . . . . . . . . . . . . . . . . . . . . 385

A. Orsatti and N. Rodino On the endomorphism ring of an infinite dimensional vector space

C. M. Ringel Some algebraically compact modules I . . . . . . . . . . . . . . . .

P. Schultz

395

419

The near endomorphism ring of an almost completely decomposable group 441

N. Snashall Reflexivity of left serial algebras . . . . . . 453

A. Tonolo On a class of minimal topological modules . . . . . . . . . . . 459

J. Trlifaj Steady rings may contain large sets of orthogonal idempotents 467

TABLE OF CONTENTS ix

P. Vamos The Holy Grail of Algebra: Seeking complete sets of invariants 475

B. C. Vinsonhaler Invariants for almost completely decomposable groups 485

J. M. Zelmanowitz A class of modules with semisimple behavior . . . . . 491

B. Zimmermann Huisgen The jinitistic dimension conjectures - a tale of 3.5 decades 501

PREFACE

On the 26th of November 1992 the organizing committee gathered together, at Luigi Salce's invitation, for the first time. The tradition of abelian groups and modules Italian conferences (Rome 77, Udine 85, Bressanone 90) needed to be kept up by one more meeting.

Since that first time it was clear to us that our goal was not so easy. In fact the main intended topics of abelian groups, modules over commutative rings and non commutative rings have become so specialized in the last years that it looked really ambitious to fit them into only one meeting. Anyway, since everyone of us shared the same mathematical roots, we did want to emphasize a common link.

So we elaborated the long symposium schedule: three days of abelian groups and three days of modules over non commutative rings with a two days' bridge of commutative algebra in between.

Many of the most famous names in these fields took part to the meeting. Over 140 participants, both attending and contributing the 18 Main Lectures and 64 Communications (see list on page xv) provided a really wide audience for an Algebra meeting.

Now that the meeting is over, we can say that our initial feeling was right. Mathematicians in different fields got the opportunity to gather together and learn what was going on "in their neighbour's yard". We do hope that in spite of the unusually hot weather we had to deal with (a very important mathematician was shouting aloud that it was "as hot as hell") all the participants got a profitable experience for their "own backyard".

Most of the articles appearing in this volume reflect the authors' contribution to the conference. All the papers, except for some of the Main Lectures, were subjected to a judgement by Referees appointed by the Editors. Unfortunately, due to the restriction on the number of pages, we had to be really selective and asked the Referees to be rather strict: sometimes we had to make painful choices, but the number of pages available was too small compared to all the papers we got. The reader will find some useful reports, by some of the Main Lectures, on the development of a particular subject. All the other papers are completely original and, in many cases, of an outstanding quality. To the Mathematical community we are sure to present on the one hand the surveys of some basic topics in Algebra and on the other hand very new results on some problems of recent interest.

Alberto Facchini and Claudia Menini

ACKNOWLEDGEMENTS

The conference on Abelian Groups and Modules was held in Padova on June 23-July 1, 1994 at the Dipartimento di Matematica Pura e Applicata of the University of Padova. We wish to thank the Director of the Department for supplying us with all the structures and technical supports we needed.

The opening session took place at the prestigious Palazzo del Bo (1542-1601), main seat of the University, founded in 1222. We wish to thank the Administration of the University of Padova for this generous concession.

We are grateful to the following organizations for their financial support: the M. U.R.S. T., Gruppo 40% "Teoria dei Gruppi e Algebra Non Commutativa", the Dipartimento di Matematica dell'UniversitO. di Ferrara, the Dipartimento di Mate­matica dell'UniversitO. di Napoli, the Dipartimento di Matematica dell'Universitd di Padova, the University of Udine, the Cassa di Risparmio di Padova e Rovigo, the Banca Popolare Veneta. In particular we are grateful to Consiglio Nazionale del­le Ricerche and to Gruppo 40% Algebra non commutativa whose financial support allowed the publication of these Proceedings.

We would especially like to thank Luigi Salce for having asked to join him in this trip and leading us out of all organizing mazes we met. Special thanks also are due to Enrico Gregorio who took care of all the 1EX-D-1EX problems. Finally we wish to thank all the colleagues that submitted us their contributions and those who have accepted to serve as referees.

In the typesetting of some of the papers the AMS-:D-'IEX and the :>W-pic macro packages were used.

ABELIAN GROUPS AND MODULES 1994 PADOVA CONFERENCE JUNE 23 - JULY 1

Scientific Committee: Gabriella D'Este, Alberto Facchini, Claudia Menini, Claudia Metelli, Luigi Salce.

Organizing Committee: Silvana Bazzoni, Riccardo Colpi, Enrico Gregorio, Luigi Salce, Paolo Zanardo.

MAIN LECTURES

P. N. Anh: AB5*, linear compactness and Morita duality D. M. Arnold: Finite rank Butler groups and near isomorphisms L. Bican: Subgroups of Butler groups P. Eklof: Classification and non-classification results for abelian groups L. Fuchs: Simple presentation K. R. Fuller: Reflexive representations of rings and algebras R. Gilmer: Zero-dimensional subrings of a commutative ring R. Gobel: Some more endomorphism rings K. Goodearl: Von Neumann regular rings and direct sum decomposition problems D. Happel: Selforthogonal modules W. Heinzer: Sub rings of finite dimensional rings P. Keef: Subfunctors of the identity on local abelian groups A. Mader: Almost completely decomposable abelian groups A. Orsatti: On the endomorphism ring of an infinite dimensional vector space C. M. Ringel: Knitting and sewing of Auslander-Reiten components P. Vamos: The Holy Grail of Algebra: searching for complete sets of invariants R. Wiegand: Rings of bounded representation type B. Zimmermann Huisgen: The geometry of uniserial representations of finite dimensional

rings

LIST OF COMMUNICATIONS

JUNE 23 K. M. Rangaswamy: Abelian groups and modules with "good" axiom-3 families O. Mutzbauer: Endomorphism rings of Reid groups A. V. Yakovlev: Mixed abelian groups with finite torsion-free rank U. Albrecht: An Azumaya theorem for a class of mixed groups P. Goeters: Warfield duality: some generalizations S. Files: Endomorphism algebras of mixed modules T. H. Fay: R-groups A. M. Sebeldin: On determination of an abelian group by its endomorphism ring

XVI

JUNE 24 C. Vinsonhaler: Completely decomposable groups

J. Irwin: Some torsion-free groups with free duals

B. Goldsmith: Isomorphic automorphism groups

E. Blagoveshchenskaya: Direct decomposition of almost completely decomposable abelian groups

L. Nongxa: Balanced and cobalanced representations of partially ordered sets

G. Calugareanu: "Amalgamations" of classes of subgroups of an abelian group

J. Krempa: Rings with periodic group of units

SATURDAY 25 M. Ouldbeddi: Finite extension of finite rank of torsion-free abelian groups

L. Koviazina: Butler groups with one r-adic relation

A. Fomin: Torsion-free a-irreducible groups of finite rank

MONDAY 27 V. Barucci: On the biggest maximally generated ideal in a semigroup ring

S. Gabelli: On the class group of a pullback

L. Salce: Generalized reflexive domains

S. Wiegand: Ranks of indecomposable modules over one-dimensional rings of finite repre-sentation type

D. Dikranjan: Uniqueness of dualities

F. V. Kuhlmann: Valuation theory for abelian groups and modules

P. Zanardo: Commutative domains large in their m-adic completion

TUESDAY 28 T. Albu: Krull dimension and localization of modular lattices

B. J. Muller: The exchange property for quasi-continuous modules

WEDNESDAY 29 R. Alfaro: On Azumaya skew group rings

J. Okninski: Graded rings with finiteness conditions

E. Jespers: Graded rings with finite support and descending chain conditions

J. Clark: Semiartinian modules and injectivity conditions

M. V. Reyes Sanchez: The relative hermitian Picard group

A. Del Rio: On the Picard group of a category of graded modules

A. Verschoren: Compatibility and sheaves

G. AbranIs: Three semigroups arising from smash product and duality constructions

C. Menini: Some results on graded modules over semigroup graded rings

I. Musson: Modules over rings of differential operators

S. Caenepeel: Categories of generalized Hopf modules

H. Krause: Ziegler spectrum and localization

T. Kucera: Structure of indecomposable injective modules over a right noetherian ring

C. Toffalori: The decision problem for lattices over a group ring

THURSDAY 30 H. Brungs: Rank one cones and valuation rings A. Del Valle Robles: Monomorphic flat envelopes I M. Saorin: Monomorphic flat envelopes II J. L. Garcia Hernandez: When is the category of fiat modules abelian If J. L. Gomez Pardo: Reflexive modules over generalizations of QF rings P. Ara: Projective modules over regular rings with S-comparability E. Pardo Espino: Refinement monoids with weak comparability and applications D. Herbera: The 0re condition for polynomial rings J. Jirasko: Large subdirect products of relative flat modules I. Assem: Fundamental groups of triangular algebras A. Tonolo: Minimal topological modules N. Snashall: QF algebras and reflexivity J. Dauns: Submodule structure of modules J. Trlifaj: Whitehead test modules T. Kepka: Slender modules

FRIDAY 1 A. Skowronski: Sode deformations of selfinjective Arlin algebras D. Zacharia: On algebras with finite Hochschild dimension L. Angeleri Hugel: Generating the category of modules without projective summands P. Draxler: Generalized one-point extensions of algebras A. Dean: Torsion-free, divisible modules for algebras with separating families G. D'Este: Torsion theories without nice symmetries R. Colpi: Tilting modules and tilting torsion theories

XVll

A. Facchini: Endomorphism rings of arlinian modules: the answer to a question posed by Krull in 1932

LIST OF PARTICIPANTS ABRAMS, Gene, Dept. of Mathematics, University of Colorado, COLORADO SPRINGS, CO 80907

(USA) ALBRECHT, Ulrich, Dept. of Mathematics, Auburn University, AUBURN, AL 36849 (USA),

germany@ducvax.auburn.edu ALBU, Toma, Facultatea Matematica, Universitatea Bucure§ti, Str. Academiei 14, 70109 BUCHAREST

(ROMANIA) ALFARO, Ricardo, Mathematics Dept., University of Michigan-Flint, FLINT, MI 48502 (USA),

alfaro..r@msb.flint.umich.edu ANGELERI HUGEL, Lidia •. Fakultat fUr Mathematik, Ludwig Maximilians Universitiit,

Therensienstr. 39, 8 MUNCHEN 2 (GERMANY) ANH, Pham Ngoc, Mathematical Institute, Hungarian Academy of Science, Realtanoda 13.15,

BUDAPEST H-1364 (HUNGARY), H1567Pha@huella.bitnet ARA, Pere, Dept. of Mathematics, Universitat Autonoma de Barcelona, 08193 BARCELONA (SPAIN),

imat8@cc.uab.es ARNOLD, David M., Mathematics Dept., Baylor University, WACO, TX 76798-7328 (USA),

Arnoldd@baylor.edu ASENSIO MAYOR, Jose, Dep. de Matematicas, Universidad de Murcia, MURCIA (SPAIN) ASSEM, Ibrahim, Dep. Mathematiques et Informatique, Universite de Sherbrooke, Sherbrooke, Quebec

J1K 2R1 (CANADA) BARUCCI, Valentina, Dip. di Matematica "Guido Castelnuovo", Universita "La Sapienza", Piazzale

Aldo Moro 2, 00185 ROMA (ITALY) BAZZONI, Silvana, Dip. di Matematica, Universita di Padova, via Belzoni 7,35131 PADOVA (ITALY),

bazzoni@pdmatl.math.unipd.it BEN ABDALLAH, Khalid, Dep.of Mathematics and Statistics, University of Montreal, MONTREAL

H3C 3J7 (CANADA), benabdal@ere.umontreal.ca

xviii

BICAN, Ladislav, Matematicko Fyzikalni Fakulta, Universita Karlova, Sokolovska 83, PRAHA 8, Karlin (CZECH REPUBLIC), bican@karlin.mff.cuni.cz

BLAGOVESHCHENSKAYA, Ekaterina, Dept. of Mathematics, St. Petersburg Polytechnic Institute, Polytecnicheskaya 29, 195251 ST. PETERSBURG (RUSSIA), kat@iiii.spb.su

BRUNGS, Hans H., Dept. of Mathematics, University of Alberta, EDMONTON, ALBERTA T6G 2G1 (CANADA)

BURGESS, Walter, Dept. of Mathematics, University of Ottawa, OTTAWA, ONTARIO K1N 6N5 (CANADA), wdbsg@acadvml.uottawa.ca

CAENEPEEL, Stefaan, Faculty of Applied Sciences, Free University of Brussels, Pleinlaan 2, B-1050 BRUSSEL (BELGIUM), z03001@bbrfuOl.bitnet

CALUGAREANU, Grigore, Dept. of Algebra, Faculty of mathematics, University Babes Bolyai, str. Kogalniceanu 1, 3400 CLUJ NAPOCA (ROMANIA)

CAMILLO, Victor, Dept. of Mathematics, University of Iowa, IOWA CITY, IA 52242 (USA), vcamillo@umaxc.weeg.uiowa.edu

CED6, Ferran, Dep. de Matematiques, Universitat Autonoma de Barcelona, 08193 BELLATERRA, BARCELONA (SPAIN)

CLARK, John, Dept. of Mathematics, University of Otago, P.O. Box 56, DUNEDIN (NEW ZEALAND) COLPI, Riccardo, Dip. di Matematica, Universita di Padova, via Belzoni 7, 35131 PADOVA (ITALY),

colpi@pdmat1.math.unipd.it DAUNS, John, Dept. of Mathematics, Tulane University, NEW ORLEANS, LA 70118 (USA) DEAN, Andrew P., Dept. of Mathematics, University of Oxford, OXFORD OX13LB (UNITED

KINGDOM) DEL RIO, Angel, Dep. de Matematicas, Universidad de Murcia, MURCIA (SPAIN) DEL VALLE, Alberto, Dep. de Matematicas, Universidad de Murcia, MURCIA (SPAIN) D'ESTE, Gabriella, Dip. di Matematica "Federico Enriques", Universita Statale di Milano, Via

C. Saldini 50, 20133 MILANO (ITALY) DIKRANJAN, Dikran, Dip. di Matematica e Informatica, Universita di Udine, via Zanon 6, 33100

UDINE (ITALY), dikranja@dimi.uniud.it DRAXLER, Peter, Dept. of Mathematics, University of Bielefeld, P.O.B. 8640, D-4800 BIELEFELD 1

(GERMANY) EKLOF, Paul, Dept. of Mathematics, University of California at Irvine, IRVINE, CA 92717 (USA),

peklof@math.uci.edu ELTER, Anja, Fachbereich 6, Mathematik, Universitat Essen GHS, Universitatstr., D-4300 ESSEN 1

(GERMANY) FACCHINI, Alberto, Dip. di Matematica e Informatica, Universita di Udine, via Zanon 6, 33100

UDINE (ITALY), facchini@dimi.uniud.it FAY, Temple H., Dept. of Mathematics, University of Southern Mississipi, HATTIESBURG, MS 39401

(USA), thfay@mozart.st.usm.edu FILES, Steve, Dept. of Mathematics U-9, University of Connecticut, STORRS, CONN 06269 (USA) FOMIN, Alexander, Dept. of Mathematics, Pedagogical State University, UI. Krasnoprudnaya 14,

107140 MOSCOW (RUSSIA), fomin.algebra@mpgu.msk.su FONTANA, Marco, Dip. di Matematica "Guido Castelnuovo", Universita "La Sapienza", Piazzale Aldo

Moro 2,00185 ROMA (ITALY) FUCHS, Laszlo, Dept. of Mathematics, Tulane University, NEW ORLEANS, LA 70118 (USA),

fuchs@mailhost.tcs.tulane.edu FULLER, Kent R., Dept. of Mathematics, University of Iowa, IOWA CITY, IA 52242 (USA),

kfuller@umaxc.weeg.uiowa.edu GABELLI, Stefania, Dip. di Matematica "Guido Castelnuovo", Universita "La Sapienza", Piazzale Aldo

Moro 2, 00185 ROMA (ITALY) GARCIA HERNANDEZ, Jose Luis, Dep. de Matematicas, Universidad de Murcia, 30071 MURCIA

(SPAIN) GILMER, Robert, Dept. of Mathematics, Florida State University, B-154, TALLAHASSE,

FL 32306-3027 (USA), gilmer@gauss.math.fsu.edu GIROLAMI, Florida, Dip. di Matematica, Universita di Roma "La Sapienza" , Piazzale A. Moro, 00185

ROMA (ITALY) GOBEL, Rudiger, Fachbereich 6, Mathematik, Universitat Essen GHS, Universitatstr., D-4300

ESSEN 1 (GERMANY), mat100@vm.hrz.uni-essen.de GOETERS, H. Pat, Dept. of Mathematics, Auburn University, AUBURN, AL 36849-3501 (USA) GOLDSMITH, Brendan, Dept. of Mathematics, Dublin Institute of Technology, Kevin Street,

DUBLIN 8 (EIRE), bgoldsmith@dit.ie GOLLOV A, Alena, Dept. of Algebra, Charles University, Sokolovska 83, 18600 PRAGUE 8 (CZECH

REPUBLIC), trlifaj@karlin.mff.cuni.cz GOMEZ PARDO, Jose Luis, Dept. of Algebra, University of Santiago de Compostela, 15771

SANTIAGO DE COMPOSTELA (SPAIN), pardo@seins.usc.es GOODEARL, Kenneth, Dept. of Mathematics, University of California Santa Barbara, SANTA

BARBARA, CA 93106 (USA), goodearl@math.ucsb.edu GREGORIO, Enrico, Dip. di Matematica, Universita di Catania, viale Doria 6,95121 CATANIA

(ITALY), gregorio@dipmat.unict.it GUlL, Pedro Antonio, Dep. de Matematicas, Universidad de Murcia, MURCIA (SPAIN)

HAPPEL, Dieter, Fachbereich Mathematik, Technische Universitat Chemnitz, Postfach 564, 09009 CHEMNITZ (GERMANY), happel@newton.mathematik.tu-chemnitz.de

HEINZER, William, Dept. of Mathematics, Purdue University, WEST LAFAYETTE, IND 47907 (USA), heinzer@math.purdue.edu

XIX

HERBERA, Dolores, Dept. of Mathematics, Rutgers University, NEW BRUNSWICK, NJ 08903 (USA) HERNANDEZ GIL, Jos6 Manuel, Dep. de Matematicas, Universidad de Murcia, MURCIA (SPAIN) HONDA, Kin-ya, Dept. of Mathematics, St. Paul's University, Ikebukuro, TOKYO 171 (JAPAN) IRWIN, John, Dept. of Mathematics, Wayne State University, DETROIT, MI (USA),

jirwin@waynestl.bitnet JESPERS, Eric, Dep. de Matematicas, Universidad de Murcia, MURCIA (SPAIN) JIRASKO, Josef, Dept. of Mathematics, Fac. of Civil Engineering, Czech Technical University,

Thakurova 7, 16629 PRAHA 6 (CZECH REPUBLIC) KEEF, Patrick, Dept. of Mathematics, Whitman College, WALLA WALLA, WA 99362 (USA),

keef@whitman.edu KEPKA, Tomas, Dept. of Algebra, Charles University, Sokolovska 83,18600 PRAGUE 8 (CZECH

REPUBLIC), kepka@karlin.mff.cuni.cz KOVIAZHINA, Lena, Moscow Pedagogical University, Prospect Vernadskogo 88/1, MOSCOW 117571

(RUSSIA) KOYAMA, Toshiko, Dept. of Mathematics, Ochanomizu University, Otsuka Bunkyou-Ku, TOKYO 112

(J APAN), koyama@is.ocha.ac.jp KRAUSE, Henning, Fakultat fur Mathematik, Universitat Bielefeld, Postfach 100131, 33501

BIELEFELD (GERMANY) KREMPA, Jan, Institute of Mathematics, University of Warsaw, Banacha 2,02-097 WARSAW

(POLAND), jkrempa@mimuw.edu.pl KUCERA, Thomas G., Dept. of Mathematics and Astronomy, University of Manitoba, WINNIPEG,

MANITOBA R3T 2N2 (CANADA) KUHLMANN, Franz-Viktor, Mathematisches Institut, Universitat Heidelberg, Neuenheimer Feld 288,

D-69120 HEIDELBERG (GERMANY) LE DONNE, Attilio, Dip. di Matematica, Universita di Roma, 00100 ROMA (ITALY) LEAL, Guilherme, Dep. de Matematicas, Universidad de Murcia, MURCIA (SPAIN) LIEBERT, Wolfgang, Mathematisches Institut, Technische Universitat Miinchen, D-8000 MUNCHEN

(GERMANY), wolfgang.liebert@mathematik.tu-muenchen.de LONGOBARDI, Patrizia, Dip. di Matematica e Applicazioni "Renato Cacciopoli", Universita di

Napoli, Via Cinthia, Complesso Monte S. Angelo, Edificio "T", 80126 NAPOLI (ITALY) MADER, Adolf, Dept. of Mathematics, University of Hawaii, 2565 The Mall, HONOLULU,

Hawaii 96822 (USA), adolf@math.hawaiLedu MARQUEZ HERNANDEZ, Concepcion Mercedes, Dep. of Mathematics, Universidad de La Laguna,

38271 ISLAS CAN ARIAS (SPAIN), cmarquez@ull.es MARTINEZ HERNANDEZ, Juan, Dep. de Matematicas, Universidad de Murcia, 30071 MURCIA

(SPAIN) MAY, Warren, Dept. of Mathematics, University of Arizona, TUCSON, AZ 85721 (USA),

may@math.arizona.edu MENEGAZZO, Federico, Dip. di Matematica, Universita di Padova, via Belzoni 7, 35131 PAD OVA

(ITALY), menegazzo@pdmatl.math.unipd.it MENICHETTI, Giampaolo, Dip. di Matematica, Universita di Bologna, Piazza di Porta S. Donato 5,

40127 BOLOGNA (ITALY) MENINI, Claudia, Dip. di Matematica, Universita di Ferrara, via Machiavelli 35,44100 FERRARA

(ITALY), men@ifeuniv.unife.it MERISI, Piercarlo, Dept. of Mathematics, University of Exeter, Laver Building North Park Road,

EXETER EX44QE (UNITED KINGDOM) METELLI, Claudia, Dip. di Matematica e Applicazioni "Renato Cacciopoli", Universita di Napoli, Via

Cinthia, Complesso Monte S. Angelo, Edificio "T", 80126 NAPOLI (ITALY) MEZZETTI, Gustavo, Dip. di Matematica Pura e Applicata, Universita di Padova, Via Belzoni 7, 35100

PADOVA (ITALY) MONARI MARTINEZ, Elisabetta, Dip. di Matematica Pura e Applicata, Universita di Padova, Via

Belzoni 7, 35131 PADOVA (ITALY) MUELLER, Bruno J., Dept. of Mathematics and Statistics, McMaster University, HAMILTON, Ontario

L8S4Kl (CANADA) MUSSON, Ian, Dept. of Mathematics, University of Wisconsin-Milwaukee, MILWAUKEE, WI 53201

(USA) MUTZBAUER, Otto, Mathematische Institut, Universitat Wiirzburg, WURZBURG 8700

(GERMANY), mutzbauer@vax.rz.uni-wuerzburg.de NONGXA, Loyiso, Dept. of Mathematics, University of the Western Cape, Private bag X17, 7535

BELLVILLE (SOUTH AFRICA) OKNINSKI, Jan, Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 WARSAW

(POLAND),okninski@mimuw.edu.pl ORSATTI, Adalberto, Dip. di Matematica, Universita di Padova, via Belzoni 7, 35131 PADOVA

(ITALY)

xx

OULDBEDDI, Mohamed, Dep.of Mathematics and Statistics, University of Montreal, MONTREAL H3C 3J7 (CANADA)

PARDO ESPINO, Enrique, Dep. de Matematiques, Universitat Autonoma de Barcelona, 08193 BELLATERRA, BARCELONA (SPAIN), imat8@cc.uab.es

PELLEGRINI, Silvia, Dip. di Elettronica per I'Automazione, Universitll di Brescia, Via Valotti 9, 25133 BRESCIA (ITALY)

PERERA, Francesc, Dept. of Mathematics, Universitat Autonoma de Barcelona, 08193 BARCELONA (SPAIN), imat8@cc.uab.es

PIEMONTINO, Rossana, Dip. di Matematica e Applicazioni "Renato Cacciopoli", Universitll di Napoli, Via Cinthia, Complesso Monte S. Angelo, Edificio "T", 80126 NAPOLI (ITALY)

RANGASWAMY, K. M., Dept. of Mathematics, University of Colorado, 1420 Augustin Bluffs Parkway, COLORADO SPRINGS, CO 80933-7150 (USA), kmranga@colospgs.bitnet

REYES SANCHEZ, Maria Victoria, Dep. of Mathematics, Universidad de La Laguna, 38271 ISLAS CANARIAS (SPAIN), mvreyes@ull.es

RINGEL, Claus Michael, Dept. of Mathematics, University of Bielefeld, D-4800 BIELEFELD 1 (GERMANY), ringel@mathematik.uni-bielefeld.de

RODINO, Nicola, Dip. di Matematica Pura e Applicata, Universitll di Padova, Via Belzoni 7, 35131 PADOVA (ITALY)

RODRIGUEZ GONZALEZ, Nieves, Dept. of Algebra, University of Santiago de Compostela, 15771 SANTIAGO DE COMPOSTELA (SPAIN), pardo@seins.usc.es

SALCE, Luigi, Dip. di Matematica, Universitll di Padova, via Belzoni 7, 35131 PAD OVA (ITALY), salce@pdmatl.math.unipd.it

SAORIN, Manuel, Dept. of Mathematics, Universida de Murcia, Apartedo 4021, Espinardo, MURCIA 30100 (SPAIN), msaorinc@fc.um.es

SCHLITT, Gregory, Dept. of Mathematics, McMaster University, HAMILTON (CANADA), schlitt@cs.sfu.ca

SEBELDIN, A. M., UI. Kovalihinskaya, NIZHNIJ NOVGOROD 30 KV 11 (RUSSIA) SIDDOWAY, Michael, Dept. of Mathematics, Colorado College, COLORADO SPRINGS, CO 80903

(USA) SKOWRONSKI, Andrzej, Math. Inst., Nicholas Copernicus University, Chopina 12/18, 87-100 TORUN

(POLAND) SNASHALL, Nicole, Dep. of Mathematics, University of Leicester, University Road, LEICESTER

LE17RH (UNITED KINGDOM) TAMBURINI, Chiara, Dip. di Matematica, Universitll Cattolica S. Cuore, Via Trieste 17, 25121

BRESCIA (ITALY), tam12@ibsucsc.bitnet TIBILETTI, Cesarina, Dip. di Matematica "Federico Enriques", Universitll StataIe di Milano, Via

C. Saldini 50, 20133 MILANO (ITALY), tibiletti@vmimat.mat.unimi.it TOFFALORI, Carlo, Dip. di Matematica e Fisica, Universitll di Camerino, Via Madonna delle Carceri,

62032 CAMERINO (MC) (ITALY), toffalori@camvax.unicam.it TONE, Noriko, Dept. of Mathematics, Tokyo Denki University, TOKYO (JAPAN) TONOLO, Alberto, Dip. di Matematica, Universitll di Padova, via Belzoni 7,35131 PADOVA (ITALY),

tonolo@pdmat1.math.unipd.it TRLIFAJ, Jan, Dept. of Algebra, Charles University, Sokolovska 83,18600 PRAGUE 8 (CZECH

REPUBLIC), trlifaj@karlin.mff.cuni.cz VALLA, Giuseppe, Dip. di Matematica, Universitll di Genova, Via L. B. Alberti 4, 16132 GENOVA

(ITALY), valla@cisi.unige.it VAMOS, Peter, Dept. of Mathematics, University of Exeter, North Park Road, EXETER EX44QE

(UNITED KINGDOM), p.vamos@exeter.ac.uk VERSCHOREN, Alain, Dept. of Mathematics, Univ. of Antwerp, R.U.C.A., Groenenborgerlaan 171,

B-2020 ANTWERP (BELGIUM), aver@ruca.ua.ac.be VILJOEN, Gert, Dept. of Mathematics, University of the Orange Free State, P.O.B. 339,

BLOEMFONTAIN 9300 (SOUTH AFRICA) VINSON HALER, Charles, Dept. of Mathematics, University of Connecticut, 196 Auditorium Road,

STORRS, CT 06269 (USA), vinson@uconnvm.bitnet WIEGAND, Roger, Dept. of Mathematics and Statistics, University of Nebraska, LINCOLN, NE 68588

(USA), rwiegand@mathlabOl.unl.edu WIEGAND, Sylvia, Dept. of Mathematics and Statistics, University of Nebraska, LINCOLN, NE 68588

(USA) swiegand@mathlabOl.unl.edu YAKOVLEV, Anatoly V., Dept. of Mathematics and Mechanic, University of St. Petersburg, Stary

Peterhof Bibliotechnaya pI. 2, 198904 ST. PETERSBURG (RUSSIA), yakov@hq.math.lgu.spb.su ZACHARIA, Dan, Dep. of Mathematics, Syracuse University, SYRACUSE, NY 13244 (USA) ZANARDO, Paolo, Dip. di Matematica, Universitll di Padova, via Belzoni 7,35131 PADOVA (ITALY),

pzanardo@pdmat1.math.unipd.it ZIMMERMAN HUISGEN, Birge, Dept. of Mathematics, University of California, SANTA BARBARA,

CA 93106 (USA), birge@henri.ucsb.edu