Algebras, Rings And Their Representations: Proceedings Of The International Conference on Algebras, Modules and Rings, Lisbon, Portugal, 14-18 July 2003

403 Pages·2006·15.01 MB·English

by  Catarina Santa-Clara

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ALGEBRAS, RINGS AND
THEIR REPRESENTATIONS
Proceedings of the International Conference
on Algebras, Modules and Rings
Alberto Facchini • Kent Fuller
Claus M Ringel • Catarina Santa-Clara
editors
ALGEBRAS, RINGS AND
THEIR REPRESENTATIONS
Proceedings of the International Conference
on Algebras, Modules and Rings

ALGEBRAS, RINGS AND
THEIR REPRESENTATIONS
Proceedings of the International Conference
on Algebras, Modules and Rings
Lisbon, Portugal 14-18 July 2003
editors
Alberto Facchini (Universita di Padova, Italy)
Kent Fuller (University of Iowa, USA)
ClauS M Ringel (Universitat Bielefeld, Germany)
Catarina Santa-Clara (Universidade de Lisboa, Portugal)
Cover image by courtesy of Joao Sotomayor
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ALGEBRAS, RINGS AND THEIR REPRESENTATIONS
Proceedings of the International Conference on Algebras, Modules and Rings
Copyright © 2006 by World Scientific Publishing Co. Pte. Ltd.
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CONTENTS
Introduction vii
Antonio Almeida Costa xv
Conference Participants xix
Contributors xxvii
Some Coreflective Categories of Topological Modules
Alina Alb 1
Inheritance of Primeness by Ideals in Lie Triple Systems
A. J. Calderon Martin and M. Forero Piulestdn 7
A Geometric Approach to Four-Dimensional Absolute Valued Triple
Systems
Antonio J. Calderon Martin and Cdndido Martin Gonzalez 17
Divisible Modules with Respect to a Torsion Theory
Iuliu Crivei and Septimiu Crivei 25
The Globalization Problem for Inner Automorphisms and Skolem-
Noether Theorems
Jeremy Haefner and Angel del Rio 37
Krull Monoids and Their Application in Module Theory
Alberto Facchini 53
Infinite Progenerator Sums
Alberto Facchini and Lawrence S. Levy 73
The Moduli Space and Versal Deformations of Three Dimensional
Lie Algebras
Alice Fialowski 79
Quadratic Algebras of Skew Type
Eric Jespers and Jan Okniriski 93
Representation Type of Commutative Noetherian Rings
(Introduction)
Lee Klingler and Lawrence S. Levy 113
v
VI
Corner Ring Theory: A Generalization of Peirce Decompositions, I
T. Y. Lam 153
Units, Principal Primes, and Generalizations of Factoriality
Peter Malcolmson and Frank Okoh 183
Algebra Associated with the Principal Block of Category O for
sl (C)
3
Frantisek Marko 201
Noncommutative Projective Schemes and Point Schemes
Izuru Mori 215
Quasideterminants and Right Roots of Polynomials Over Division
Rings
Barbara L. Osofsky 241
Certains Resultats sur une Extension Minimale
Mohamed Oukessou 265
•-Identities in Matrix Superalgebras with Superinvolution *
Tsetska Grigorova Rashkova 273
Structure and Representations of Conformal Algebras
Alexander Retakh 289
Actions of Tori and Finite Fans
Sonia L. Rueda 313
Homologically Induced s[(l, 2)-Modules
Jose Carlos de Sousa Oliveira Santos 329
Injective Dimension Relative to a Torsion Theory
Patrick F. Smith 343
Structure Theorems on Countably Compact Rings
M. Ursul 357
INTRODUCTION
In memory of Professor Antonio Almeida Costa,
on the centenary of his birth.
Organized by Centro de Algebra da Universidade de Lisboa
Held at Faculdade de Ciencias da Universidade de Lisboa
http://caul.cii.fc.ul.pt/lisboa2003/
In homage to Professor Antonio Almeida Costa (1903-1978), Full Pro
fessor of the Faculty of Sciences of the University of Lisbon (FCUL), and
on occasion of the 100th anniversary of his birth, the Centro de Algebra da
Universidade de Lisboa (CAUL) organized the "International Conference
on Algebras, Modules and Rings", held at FCUL, from the 14th to the 18th
of July 2003.
This event was widely publicized and attracted 151 participants, from
33 different nationalities, comprising many experts in the areas of Ring
and Module Theory, Representation Theory of Algebras, and other closely
related fields, especially Non-Commutative Algebraic Geometry. It pro
vided an excellent venue for the communication of recent results and the
discussion of new problems in the areas that will surely bring about future
progress in research.
The invited speakers consisted of 9 main speakers, each lecturing for
50 minutes, and 9 plenary speakers, speaking for 35 minutes. The main
speakers, leaders in their respective areas of research, were headed by the
keynote speaker, Michel Van den Bergh, who set the tone for the confer
ence, establishing a connection to Non-Commutative Algebraic Geometry.
The plenary speakers are younger mathematicians, with promising work
vii
viii
on the different subjects covered. The conference also included 85 short
communications (20 minutes each).
The conference was co-funded by CAUL, DMFCUL, FCUL, Fundagao
para a Ciencia e a Tecnologia, Project POCTI/143/2003 of FCT and
FEDER, Centro de Matematica da Universidade do Porto, Centro de
Estruturas Lineares e Combinatorias and Universidade Lusofona. Grants
were awarded to some participants, both by Unesco-Roste and Deutscher
Akademische Austausch Dienst. The organization enjoyed some support
from Turismo de Lisboa, Lisbon's City Council and Bookshop Escolar
Editora. Participants had discounts on flights by TAP and VARIG.
Conference Organization
Scientific Committee
A. Facchini (Padova) J. A. Green (Oxford, Warwick)
K. Puller (Iowa) C. M. Ringel (Bielefeld)
M. L. Galvao (Lisboa), coordinator D. Simson (N. Copernicus)
J. L. Gomez Pardo P. F. Smith (Glasgow)
(Santiago de Compostela)
Organizing Committee
A. P. Alexandre (Nova de Lisboa) C. Lomp (Porto)
P. Carvalho Lomp (Porto) M. T. Nogueira (Lisboa)
A. V. Fonseca (Lusofona, Leicester) C. Santa-Clara (Lisboa), coordinator
M. L. Galvao (Lisboa) M. E. Simoes (Lisboa)
Assistants to the Organization
Staff: M. Manuela Ferreira, Beatrice Huberty.
Students: Catarina Barroca, Patricia Batista, Marta Cabrita, Eliana Cas
tro, Vidal Delgado, Antonio V. Dias, M. Graga Duffner, Gilda M. Fer
reira, Susana Frederique, Jaime Gaspar, Joaquim Graga, Joana M. Matos,
Rita Monge, Alexandra Passinhas, Ana Pinheiro, David Raimundo, Filipe
Ramos, Andrea Rodrigues, Carina Rodrigues, Ana Isabel Teixeira, Ana
Margarida Troncao.
ix
Invited Talks
Keynote
M. Van den Bergh (Limburgs-Diepenbeek): Derived categories in algebraic geom
etry
Main Talks
S. Koenig (Leicester): Comparing Schur algebras, upwards and downwards
T.-Y. Lam (California, Berkeley): Corner Ring Theory: A Generalization of Peirce
Decompositions
L. Levy (Nebraska, Lincoln and Wisconsin, Madison): Representation type of
Commutative Noetherian Rings
0. Mathieu (Claude Bernard, Lyon): Connection on stable bundle
B. Osofsky (Rutgers, New Brunswick): Quasideterminants and Roots of Polyno
mials over Division Rings
C. M. Ringel (Bielefeld): Basic properties of the module category of an artin algebra
M. Saorin (Murcia): Categorical invariance of automorphism groups of rings an al
gebras
J. Trlifaj (Karlova, Praha): Cotorsion pairs
Plenary Talks
P. Ara (Autonoma, Barcelona): Finitely presented modules over Leavitt algebras
J. A. de la Pena (UNAM, Mexico City): Hochschild cohomology of algebras and
epimorphisms
1. Gordon (Glasgow): Rational Cherednik algebras and applications
P. A. Guil Asensio (Murcia): Left Cotorsion Rings
O. Iyama (Himeji): Representation dimension of artin algebras
J. Okniriski (Warsaw): Quadratic algebras of skew type
C. Santa-Clara (Lisboa): Goldie dimension applied to Linear Operator Theory
J. Schroer (Leeds): A decomposition theory for irreducible components of module
varieties
A. Tonolo (Padova): Cotilting modules versus canonical modules for Cohen-Macaulay
rings
Contributed talks
Module Theory
Klaus Robert Aehle: Complexity of degenerations of modules
Khaled Al-Takhman: Comatrix Corings
Lidia Angeleri Hugel: Tilting modules and Gorenstein rings
Maria Jose Arroyo Paniagua: Spectral Torsion Theories and a General Theory of
Types
Septimiu Crivei: On divisible modules with respect to a torsion theory
Sergio Estrada: Torsion free covers of cotorsion modules
Alberto Facchini: Projective modules and divisor homomorphisms
Grigory Garkusha: Triangulated categories and the Ziegler spectrum
Enrico Gregorio: Cotilting dualities