Ring theory and algebraic geometry : proceedings of the fifth international conference (SAGA V) in León, Spain

351 Pages·2001·17 MB·English

by  Ángel Granja, José Ángel Hermida, A Verschoren

ring theory and
algebraic geometry
ring theory and
algebraic geometry
proceedings of the fifth international
conference (SAGA V) in León, Spain
edited by
Ángel Granja
University of León
León, Spain
José Ángel Hermida
University of León
León, Spain
Alain Verschoren
University of Antwerp, RUCA
Antwerp, Belgium
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PUREANDAPPLIEDMATHEMATICS
AProgramofMonographs,Textbooks,andLectureNotes
EXECUTIVEEDITORS
EarlJ.Taft ZuhairNashed
RutgersUniversity UniversityofCentralFlorida
NewBrunswick,NewJersey Orlando,Florida
EDITORIALBOARD
M.S.Baouendi AnilNerode
UniversityofCalifornia, CornellUniversity
SanDiego
DonaldPassman
JaneCronin UniversityofWisconsin,
RutgersUniversity Madison
JackK.Hale FredS.Roberts
GeorgiaInstituteofTechnology RutgersUniversity
S.Kobayashi DavidL.Russell
UniversityofCalifornia, VirginiaPolytechnicInstitute
Berkeley andStateUniversity
MarvinMarcus WalterSchempp
UniversityofCalifornia, UniversitätSiegen
SantaBarbara
MarkTeply
W.S.Massey UniversityofWisconsin,
YaleUniversity Milwaukee
LECTURENOTESINPUREANDAPPLIEDMATHEMATICS
1. N.Jacobson,ExceptionalLieAlgebras
2. L.-Å.LindahlandF.Poulsen,ThinSetsinHarmonicAnalysis
3. I.Satake,ClassificationTheoryofSemi-SimpleAlgebraicGroups
4. F.Hirzebruchetal.,DifferentiableManifoldsandQuadraticForms
5. I.Chavel,RiemannianSymmetricSpacesofRankOne
6. R.B.Burckel,CharacterizationofC(X)AmongItsSubalgebras
7. B.R.McDonaldetal.,RingTheory
8. Y.-T.Siu,TechniquesofExtensiononAnalyticObjects
9. S.R.Caradusetal.,CalkinAlgebrasandAlgebrasofOperatorsonBanachSpaces
10. E.O.Roxinetal.,DifferentialGamesandControlTheory
11. M.OrzechandC.Small,TheBrauerGroupofCommutativeRings
12. S.Thomier,TopologyandItsApplications
13. J.M.LopezandK.A.Ross,SidonSets
14. W.W.ComfortandS.Negrepontis,ContinuousPseudometrics
15. K.McKennonandJ.M.Robertson,LocallyConvexSpaces
16. M.CarmeliandS.Malin,RepresentationsoftheRotationandLorentzGroups
17. G.B.Seligman,RationalMethodsinLieAlgebras
18. D.G.deFigueiredo,FunctionalAnalysis
19. L.Cesarietal.,NonlinearFunctionalAnalysisandDifferentialEquations
20. J.J.Schäffer,GeometryofSpheresinNormedSpaces
21. K.YanoandM.Kon,Anti-InvariantSubmanifolds
22. W.V.Vasconcelos,TheRingsofDimensionTwo
23. R.E.Chandler,HausdorffCompactifications
24. S.P.FranklinandB.V.S.Thomas,Topology
25. S.K.Jain,RingTheory
26. B.R.McDonaldandR.A.Morris,RingTheoryII
27. R.B.MuraandA.Rhemtulla,OrderableGroups
28. J.R.Graef,StabilityofDynamicalSystems
29. H.-C.Wang,HomogeneousBranchAlgebras
30. E.O.Roxinetal.,DifferentialGamesandControlTheoryII
31. R.D.Porter,IntroductiontoFibreBundles
32. M.Altman,ContractorsandContractorDirectionsTheoryandApplications
33. J.S.Golan,DecompositionandDimensioninModuleCategories
34. G.Fairweather,FiniteElementGalerkinMethodsforDifferentialEquations
35. J.D.Sally,NumbersofGeneratorsofIdealsinLocalRings
36. S.S.Miller,ComplexAnalysis
37. R.Gordon,RepresentationTheoryofAlgebras
38. M.GotoandF.D.Grosshans,SemisimpleLieAlgebras
39. A.I.Arrudaetal.,MathematicalLogic
40. F.VanOystaeyen,RingTheory
41. F.VanOystaeyenandA.Verschoren,ReflectorsandLocalization
42. M.Satyanarayana,PositivelyOrderedSemigroups
43. D.LRussell,MathematicsofFinite-DimensionalControlSystems
44. P.-T.LiuandE.Roxin,DifferentialGamesandControlTheoryIII
45. A.GeramitaandJ.Seberry,OrthogonalDesigns
46. J. Cigler, V. Losert, and P. Michor, Banach Modules and Functors on Categories of Banach
Spaces
47. P.-T.LiuandJ.G.Sutinen,ControlTheoryinMathematicalEconomics
48. C.Byrnes,PartialDifferentialEquationsandGeometry
49. G.Klambauer,ProblemsandPropositionsinAnalysis
50. J.Knopfmacher,AnalyticArithmeticofAlgebraicFunctionFields
51. F.VanOystaeyen,RingTheory
52. B.Kadem,BinaryTimeSeries
53. J.Barros-NetoandR.A.Artino,HypoellipticBoundary-ValueProblems
54. R.L.Sternbergetal.,NonlinearPartialDifferentialEquationsinEngineeringandAppliedScience
55. B.R.McDonald,RingTheoryandAlgebraIII
56. J.S.Golan,StructureSheavesOveraNoncommutativeRing
57. T.V.Narayanaetal.,Combinatorics,RepresentationTheoryandStatisticalMethodsinGroups
58. T.A.Burton,ModelingandDifferentialEquationsinBiology
59. K.H.KimandF.W.Roush,IntroductiontoMathematicalConsensusTheory
60. J.BanasandK.Goebel,MeasuresofNoncompactnessinBanachSpaces
61. O.A.Nielson,DirectIntegralTheory
62. J.E.Smithetal.,OrderedGroups
63. J.Cronin,MathematicsofCellElectrophysiology
64. J.W.Brewer,PowerSeriesOverCommutativeRings
65. P.K.KamthanandM.Gupta, SequenceSpacesandSeries
66. T.G.McLaughlin,RegressiveSetsandtheTheoryofIsols
67. T.L.Herdmanetal.,IntegralandFunctionalDifferentialEquations
68. R.Draper,CommutativeAlgebra
69. W. G. McKay and J. Patera, Tables of Dimensions, Indices, and Branching Rules for Repre-
sentationsofSimpleLieAlgebras
70. R.L.DevaneyandZ.H.Nitecki,ClassicalMechanicsandDynamicalSystems
71. J.VanGeel,PlacesandValuationsinNoncommutativeRingTheory
72. C.Faith,InjectiveModulesandInjectiveQuotientRings
73. A.Fiacco,MathematicalProgrammingwithDataPerturbationsI
74. P.Schultzetal.,AlgebraicStructuresandApplications
75. LBicanetal.,Rings,Modules,andPreradicals
76. D.C.KayandM.Breen,ConvexityandRelatedCombinatorialGeometry
77. P.FletcherandW.F.Lindgren,Quasi-UniformSpaces
78. C.-C.Yang,FactorizationTheoryofMeromorphicFunctions
79. O.Taussky,TernaryQuadraticFormsandNorms
80. S.P.SinghandJ.H.Burry,NonlinearAnalysisandApplications
81. K.B.Hannsgenetal.,VolterraandFunctionalDifferentialEquations
82. N.L.Johnsonetal.,FiniteGeometries
83. G.I.Zapata,FunctionalAnalysis,Holomorphy,andApproximationTheory
84. S.GrecoandG.Valla,CommutativeAlgebra
85. A.V.Fiacco,MathematicalProgrammingwithDataPerturbationsII
86. J.-B.Hiriart-Urrutyetal.,Optimization
87. A.FigaTalamancaandM.A.Picardello,HarmonicAnalysisonFreeGroups
88. M.Harada,FactorCategorieswithApplicationstoDirectDecompositionofModules
89. V.I.Istra'tescu,StrictConvexityandComplexStrictConvexity
90. V.Lakshmikantham,TrendsinTheoryandPracticeofNonlinearDifferentialEquations
91. H.L.ManochaandJ.B.Srivastava,AlgebraandItsApplications
92. D. V. Chudnovsky and G. V. Chudnovsky, Classical and Quantum Models and Arithmetic
Problems
93. J.W.Longley,LeastSquaresComputationsUsingOrthogonalizationMethods
94. L.P.deAlcantara,MathematicalLogicandFormalSystems
95. C.E.Aull,RingsofContinuousFunctions
96. R.Chuaqui,Analysis,Geometry,andProbability
97. L.FuchsandL.Salce,ModulesOverValuationDomains
98. P.FischerandW.R.Smith,Chaos,Fractals,andDynamics
99. W.B.PowellandC.Tsinakis,OrderedAlgebraicStructures
100. G. M. Rassias and T. M. Rassias, Differential Geometry, Calculus of Variations, and Their
Applications
101. R.-E.HoffmannandK.H.Hofmann,ContinuousLatticesandTheirApplications
102. J.H.LightbourneIIIandS.M.RankinIII,PhysicalMathematicsandNonlinearPartialDifferential
Equations
103. C.A.BakerandL.M.Batten,FiniteGeometrics
104. J.W.Breweretal.,LinearSystemsOverCommutativeRings
105. C.McCroryandT.Shifrin,GeometryandTopology
106. D.W.Kuekeetal.,MathematicalLogicandTheoreticalComputerScience
107. B.-L.LinandS.Simons,NonlinearandConvexAnalysis
108. S.J.Lee,OperatorMethodsforOptimalControlProblems
109. V.Lakshmikantham,NonlinearAnalysisandApplications
110. S.F.McCormick,MultigridMethods
111. M.C.Tangora,ComputersinAlgebra
112. D.V.ChudnovskyandG.V.Chudnovsky,SearchTheory
113. D.V.ChudnovskyandR.D.Jenks,ComputerAlgebra
114. M.C.Tangora,ComputersinGeometryandTopology
115. P.Nelsonetal.,TransportTheory,InvariantImbedding,andIntegralEquations
116. P.Clémentetal.,SemigroupTheoryandApplications
117. J.Vinuesa,OrthogonalPolynomialsandTheirApplications
118. C.M.Dafermosetal.,DifferentialEquations
119. E.O.Roxin,ModernOptimalControl
120. J.C.Díaz,MathematicsforLargeScaleComputing
121. P.S.MilojevicÚ,NonlinearFunctionalAnalysis
122. C.Sadosky,AnalysisandPartialDifferentialEquations
123. R.M.Shortt,GeneralTopologyandApplications
124. R.Wong,AsymptoticandComputationalAnalysis
125. D.V.ChudnovskyandR.D.Jenks,ComputersinMathematics
126. W.D.Wallisetal.,CombinatorialDesignsandApplications
127. S.Elaydi,DifferentialEquations
128. G.Chenetal.,DistributedParameterControlSystems
129. W.N.Everitt,Inequalities
130. H. G. Kaper and M. Garbey, Asymptotic Analysis and the Numerical Solution of Partial Differ-
entialEquations
131. O.Arinoetal.,MathematicalPopulationDynamics
132. S.Coen,GeometryandComplexVariables
133. J. A. Goldstein et al., Differential Equations with Applications in Biology, Physics, and
Engineering
134. S.J.Andimaetal.,GeneralTopologyandApplications
135. PClémentetal.,SemigroupTheoryandEvolutionEquations
136. K.Jarosz,FunctionSpaces
137. J.M.Bayodetal.,p-adicFunctionalAnalysis
138. G.A.Anastassiou,ApproximationTheory
139. R.S.Rees,Graphs,Matrices,andDesigns
140. G.Abramsetal.,MethodsinModuleTheory
141. G.L.MullenandP.J.-S.Shiue,FiniteFields,CodingTheory,andAdvancesinCommunications
andComputing
142. M.C.JoshiandA.V.Balakrishnan,MathematicalTheoryofControl
143. G.KomatsuandY.Sakane,ComplexGeometry
144. I.J.Bakelman,GeometricAnalysisandNonlinearPartialDifferentialEquations
145. T.MabuchiandS.Mukai,EinsteinMetricsandYang–MillsConnections
146. L.FuchsandR.Göbel,AbelianGroups
147. A.D.PollingtonandW.Moran,NumberTheorywithanEmphasisontheMarkoffSpectrum
148. G.Doreetal.,DifferentialEquationsinBanachSpaces
149. T.West,ContinuumTheoryandDynamicalSystems
150. K.D.Bierstedtetal.,FunctionalAnalysis
151. K.G.Fischeretal.,ComputationalAlgebra
152. K.D.Elworthyetal.,DifferentialEquations,DynamicalSystems,andControlScience
153. P.-J.Cahen,etal.,CommutativeRingTheory
154. S.C.CooperandW.J.Thron,ContinuedFractionsandOrthogonalFunctions
155. P.ClémentandG.Lumer,EvolutionEquations,ControlTheory,andBiomathematics
156. M.GyllenbergandL.Persson,Analysis,Algebra,andComputersinMathematicalResearch
157. W.O.Brayetal.,FourierAnalysis
158. J.BergenandS.Montgomery,AdvancesinHopfAlgebras
159. A.R.Magid,Rings,Extensions,andCohomology
160. N.H.Pavel,OptimalControlofDifferentialEquations
161. M.Ikawa,SpectralandScatteringTheory
162. X.LiuandD.Siegel,ComparisonMethodsandStabilityTheory
163. J.-P.Zolésio,BoundaryControlandVariation
164. M.Kr'íz''eketal.,FiniteElementMethods
165. G.DaPratoandL.Tubaro,ControlofPartialDifferentialEquations
166. E.Ballico,ProjectiveGeometrywithApplications
167. M.Costabeletal.,BoundaryValueProblemsandIntegralEquationsinNonsmoothDomains
168. G.Ferreyra,G.R.Goldstein,andF.Neubrander,EvolutionEquations
169. S.Huggett,TwistorTheory
170. H.Cooketal.,Continua
171. D.F.AndersonandD.E.Dobbs,Zero-DimensionalCommutativeRings
172. K.Jarosz,FunctionSpaces
173. V.Anconaetal.,ComplexAnalysisandGeometry
174. E.Casas,ControlofPartialDifferentialEquationsandApplications
175. N.Kaltonetal.,InteractionBetweenFunctionalAnalysis,HarmonicAnalysis,andProbability
176. Z.Dengetal.,DifferentialEquationsandControlTheory
177. P.Marcellinietal.PartialDifferentialEquationsandApplications
178. A.Kartsatos,TheoryandApplicationsofNonlinearOperatorsofAccretiveandMonotoneType
179. M.Maruyama,ModuliofVectorBundles
180. A.UrsiniandP.Aglianò,LogicandAlgebra
181. X.H.Caoetal.,Rings,Groups,andAlgebras
182. D.ArnoldandR.M.Rangaswamy,AbelianGroupsandModules
183. S.R.ChakravarthyandA.S.Alfa,Matrix-AnalyticMethodsinStochasticModels
184. J.E.Andersenetal.,GeometryandPhysics
185. P.-J.Cahenetal.,CommutativeRingTheory
186. J.A.Goldsteinetal.,StochasticProcessesandFunctionalAnalysis
187. A.Sorbi,Complexity,Logic,andRecursionTheory
188. G. Da Prato and J.-P. Zolésio, Partial Differential Equation Methods in Control and Shape
Analysis
189. D.D.Anderson,FactorizationinIntegralDomains
190. N.L.Johnson,MostlyFiniteGeometries
191. D.HintonandP.W.Schaefer,SpectralTheoryandComputationalMethodsofSturm–Liouville
Problems
192. W.H.Schikhofetal.,p-adicFunctionalAnalysis
193. S.Sertöz,AlgebraicGeometry
194. G.CaristiandE.Mitidieri,ReactionDiffusionSystems
195. A.V.Fiacco,MathematicalProgrammingwithDataPerturbations
196. M.Kr'íz''eket al., Finite Element Methods: Superconvergence, Post-Processing, and A
PosterioriEstimates
197. S.CaenepeelandA.Verschoren,Rings,HopfAlgebras,andBrauerGroups
198. V.Drenskyetal.,MethodsinRingTheory
199. W.B.JonesandA.SriRanga,OrthogonalFunctions,MomentTheory,andContinuedFractions
200. P.E.Newstead,AlgebraicGeometry
201. D.DikranjanandL.Salce,AbelianGroups,ModuleTheory,andTopology
202. Z.Chenetal.,AdvancesinComputationalMathematics
203. X.CaicedoandC.H.Montenegro,Models,Algebras,andProofs
204. C.Y.Yéldérém andS.A.Stepanov,NumberTheoryandItsApplications
205. D.E.Dobbsetal.,AdvancesinCommutativeRingTheory
206. F.VanOystaeyen,CommutativeAlgebraandAlgebraicGeometry
207. J.Kakoletal.,p-adicFunctionalAnalysis
208. M.BoulagouazandJ.-P.Tignol,AlgebraandNumberTheory
209. S.CaenepeelandF.VanOystaeyen,HopfAlgebrasandQuantumGroups
210. F. Van Oystaeyen and M. Saorin, Interactions Between Ring Theory and Representations of
Algebras
211. R.Costaetal.,NonassociativeAlgebraandItsApplications
212. T.-X.He,WaveletAnalysisandMultiresolutionMethods
213. H.HudzikandL.Skrzypczak,FunctionSpaces: TheFifthConference
214. J.Kajiwaraetal.,FiniteorInfiniteDimensionalComplexAnalysis
215. G.LumerandL.Weis,EvolutionEquationsandTheirApplicationsinPhysicalandLifeSciences
216. J.Cagnoletal.,ShapeOptimizationandOptimalDesign
217. J.HerzogandG.Restuccia,GeometricandCombinatorialAspectsofCommutativeAlgebra
218. G.Chenetal.,ControlofNonlinearDistributedParameterSystems
219. F.AliMehmetietal.,PartialDifferentialEquationsonMultistructures
220. D.D.AndersonandI.J.Papick,IdealTheoreticMethodsinCommutativeAlgebra
221. Á.Granjaetal.,RingTheoryandAlgebraicGeometry
222. A.K.Katsarasetal.,p-adicFunctionalAnalysis
223. R.Salvi,TheNavier-StokesEquations
224. F.U.CoelhoandH.A.Merklen,RepresentationsofAlgebras
225. S.AizicoviciandN.H.Pavel,DifferentialEquationsandControlTheory
226. G.Lyubeznik,LocalCohomologyandItsApplications
227. G.DaPratoandL.Tubaro,StochasticPartialDifferentialEquationsandApplications
228. W.A.Carniellietal.,Paraconsistency
229. A.BenkiraneandA.Touzani,PartialDifferentialEquations
230. A.Illanesetal.,ContinuumTheory
231. M.Fontanaetal.,CommutativeRingTheoryandApplications
232. D.MondandM.J.Saia,RealandComplexSingularities
233. V.AnconaandJ.Vaillant,HyperbolicDifferentialOperators
AdditionalVolumesinPreparation
Preface
The Fifth International Conference on Algebra and Algebraic Geometry (SAGA V)
was held at the University of Leon (Spain) and contributors and participants origi-
nated from more than 15 European and non-European countries. As in earlier ver-
sions of these meetings in Antwerp, Santiago de Compostela, Puerto de la Cruz and
Brussels, talks concentrated on algebraic and geometric subjects, with particular
emphasis on intrinsic links between these domains. The main speakers were P. Ara
(Barcelona), A. Bak (Bielefeld), A. Campillo (Valladolid), T. Lenagan (Edinburgh),
M.P. Malliavin (Paris VI), F. Van Oystaeyen (Antwerp), A. del Rio (Murcia), M.
Spivakovsky (Toronto) and V. W. Vasconcelos (Rutgers). The Scientific Committee
consisted of J. L. Bueso, S. Caenepeel, J.A. Hermida, T. Sanchez-Giralda, A. Ver-
schorcn and E. Villanueva. The Organizing Committee consisted of A. de Francisco,
A. Granja and J. Susperregui. The organizers would like to thank the University of
Leon, the Junta de Castilla Leon and Caja Espana for financial and logistic support.
The meeting was also partially sponsored by the grants DGICYT PB95-0603-C02
and LE 36/98. Our particular thanks go to the "locals", M. Carriegos, J. Gomez,
M. Lopez and C. Sanchez whose youthful enthusiasm helped to solve all practical
problems, large and small during the meeting, to Stef Caenepel, whose capacities as
an entertainer played a fundamental role during the meeting (as always) and, last
but not least, to the secretaries of Department of Mathematics, Ana del Rio and
Ana Robles. We hope the participants enjoyed this meeting as much as we did!
Angel Granja
Jose Angel Hermida
Alain Verschoren
Copyright ©2001 by Marcel Dekker,Inc. All Rights Reserved.
Preface
Contributors
Conference Participants
1. Frobenius and Maschke Type Theorems for Doi-Hopf Modules and
Entwined Modules Revisited: A Unified Approach
T. Brzezinski, S. Caenepeel, G. Militaru and S. Zhu
2. Computing the Gelfand-Kirillov Dimension II
J. L. Bueso, J. Gomez-Torrecillas, and F. J. Lobillo
3. Some Problems About Nilpotent Lie Algebras
J. M. Cabezas, L. M. Camacho, J, R. Gomez, A. Jimenez-Merchdn,
E. Pastor, J. Reyes, and I. Rodriguez
4. On L*-Triples and Jordan //*-Pairs
A. J. Calderon-Martin and C. Martin-Gonzdlez
5. Toric Mathematics from Semigroup Viewpoint
A. Campillo and P. Pison
6. Canonical Forms for Linear Dynamical Systems over Commutative
Rings: The Local Case
M. Carriegos and T. Sdnchez-Giralda
1. An Introduction to Janet Bases and Grobner Bases
F. J. Castro-Jimenez and M. A. Moreno-Frias
8. Invariants of Coalgebras
J. Cuadra and F. Van Oystaeyen
9. Multiplication Objects
J. Escoriza and B. Torrecillas
10. Krull-Schmidt Theorem and Semilocal Endormorphism Rings
A. Facchini
11. On Suslin's Stability Theorem for R[x,..,x ]
r m
J. Gago-Vargas
12. Characterization of Rings Using Socle-Fine and Radical-Fine Notions
C. M. Gonzdlez, A. Idelhadj, and A. Yahya
13. About Bernstein Algebras
S. Gonzdlez and C. Martinez
Copyright ©2001 by Marcel Dekker,Inc. All Rights Reserved.