ideal theoretic methods in commutative algebra PURE AND APPLIED MATHEMATICS A Program of Monographs, Textbooks, and Lecture Notes EXECUTIVE EDITORS Earl J. Taft Zuhair Nashed Rutgers University University of Delaware New Brunswick, New Jersey Newark, Delaware EDITORIAL BOARD M. S. Baouendi Anil Nerode University of California, Cornell University San Diego Donald Passman Jane Cronin University of Wisconsin, Rutgers University Madison Jack K.Hale Fred S. Roberts Georgia Institute of Technology Rutgers University S. Kobayashi David L. Russell University of California, Virginia Polytechnic Institute Berkeley and State University Marvin Marcus Walter Schempp University of California, Univers i tàt Siegen Santa Barbara Mark Teply W. S. Massey University of Wisconsin, Yale University Milwaukee LECTURE NOTES IN PURE AND APPLIED MATHEMATICS 1. N. Jacobson, ExceptionalLieAlgebras 2. L-A Lindahl and F. Poulsen,ThinSetsinHarmonicAnalysis 3. /. Satake, ClassificationTheoryofSemi-SimpleAlgebraicGroups 4. F. Hlrzebruch et al., Differentiate Manifolds and Quadratic Forms 5. /. Chavel, RiemannianSymmetricSpacesofRankOne 6. R. B. Burckel, CharacterizationofC(X)AmongItsSubalgebras 7. B. R. McDonald et al., RingTheory 8. Y.-T. Siu,TechniquesofExtensiononAnalyticObjects 9. S. R. Caradus et al., CalkinAlgebrasandAlgebrasofOperatorsonBanachSpaces 10. E.O. Roxin et al., DifferentialGamesandControlTheory 11. M. Orzech and C. Small,TheBrauerGroupofCommutativeRings 12. S. Thornier,TopologyandItsApplications 13. J. M. Lopez and K. A. Ross, SidonSets 14. W. W. Comfort and S. Negrepontis, ContinuousPseudometrics 15. K. McKennon and J. M. Robertson, LocallyConvexSpaces 16. M. Carmeli and S. Malin, RepresentationsoftheRotationandLorentzGroups 17. G. B. Seligman, RationalMethodsinLieAlgebras 18. D. G. de Figueiredo, FunctionalAnalysis 19. L Cesan et al., NonlinearFunctionalAnalysisandDifferentialEquations 20. J. J. Schâffer, GeometryofSpheresinNormedSpaces 21. K. Yano and M. Kon,Anti-InvariantSubmanifolds 22. W. V. Vasconcelos,TheRingsofDimensionTwo 23. R. E. Chandler, HausdorffCompactifications 24. S. P. Franklin and B. V. S. Thomas,Topology 25. S. K. Jain, RingTheory 26. R R. McDonald and R. A. Mom's, RingTheoryII 27. R. B. Mura and A. Rhemtulla,OrderableGroups 28. J. R. Graef, StabilityofDynamicalSystems 29. H.-C. Wang, HomogeneousBranchAlgebras 30. E. O. Roxin et al., 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. Goto and F. D. Grosshans, SemisimpleLieAlgebras 39. A. I. Arruda et al., MathematicalLogic 40. F. Van Oystaeyen, RingTheory 41. F. Van Oystaeyen and A. Verschoren, ReflectorsandLocalization 42. M. Satyanarayana, PositivelyOrderedSemigroups 43. D. L Russell, MathematicsofFinite-DimensionalControlSystems 44. P.-T. Liu andE. Roxin, DifferentialGamesandControlTheoryIII 45. A. Geramita and J. Seberry, OrthogonalDesigns 46. J. Cigler, V. Losert, and P. Michor, Banach Modules and Functors onCategories of Banach Spaces 47. P.-T. Liu and J. G. Sutinen, ControlTheoryinMathematicalEconomics 48. C. Byrnes, PartialDifferentialEquationsandGeometry 49. G. Klambauer, ProblemsandPropositionsinAnalysis 50. J. Knopfmacher, AnalyticArithmeticofAlgebraicFunctionFields 51. F. Van Oystaeyen, RingTheory 52. B. Kadem, BinaryTimeSeries 53. J. Barros-Neto and R. A. Artino, HypoellipticBoundary-ValueProblems 54. R. L. Sternberg et al., NonlinearPartialDifferentialEquationsinEngineeringandAppliedScience 55. B. R. McDonald, RingTheoryandAlgebraIII 56. J. S. Golan, StructureSheavesOveraNoncommutativeRing 57. T. V. Narayana et al., Combinatorics,RepresentationTheoryandStatisticalMethodsinGroups 58. T. A. Burton, ModelingandDifferentialEquationsinBiology 59. K. H. Kim and F. W. Roush, IntroductiontoMathematicalConsensusTheory 60. J. Bañas and K. Goebel,MeasuresofNoncompactness inBanachSpaces 61. O. A. Nielson,DirectIntegralTheory 62. J. E. Smith et al.,OrderedGroups 63. J. Cronin,MathematicsofCellElectrophysiology 64. J.W. Brewer, PowerSeriesOverCommutativeRings 65. P. K Kamthan and M. Gupta, SequenceSpacesandSeries 66. T.G. McLaughlin,RegressiveSetsandtheTheoryofIsols 67. T. L Herdman et al.,IntegralandFunctionalDifferential Equations 68. R. Draper, CommutativeAlgebra 69. W. G. McKay and J. Patera,Tables of Dimensions, Indices, and Branching Rules for Repre- sentationsofSimpleLieAlgebras 70. R. L Devaney and Z. H. Nitecki, ClassicalMechanicsandDynamicalSystems 71. J. Van Geel, PlacesandValuationsinNoncommutative RingTheory 72. C. Faith,InjectiveModulesandInjectiveQuotientRings 73. A. Fiacco,MathematicalProgrammingwithDataPerturbationsI 74. P. Schultz et al., AlgebraicStructuresandApplications 75. L Bican et al.,Rings,Modules,andPreradicals 76. D. C. Kay and M. Breen,ConvexityandRelatedCombinatorialGeometry 77. P. Fletcher and W. F. Lindgren,Quasi-UniformSpaces 78. C.-C. Yang,FactorizationTheoryofMeromorphic Functions 79. O. Taussky, TernaryQuadraticFormsandNorms 80. S. P. Singh and J. H. Burry, NonlinearAnalysisandApplications 81. K. B. Hannsgen et al., VolterraandFunctionalDifferential Equations 82. N. L. Johnson et al.,FiniteGeometries 83. G./. Zapata,FunctionalAnalysis,Holomorphy,andApproximationTheory 84. S. Greco and G. Valla, CommutativeAlgebra 85. A. V. Fiacco,MathematicalProgrammingwithDataPerturbationsII 86. J.-B. Hiriart-Urrutyetal., Optimization 87. A. Figa Talamanca and M. A. Picardello,HarmonicAnalysisonFreeGroups 88. M. Harada,FactorCategorieswithApplicationstoDirectDecompositionofModules 89. V. I. Istràtescu,StrictConvexityandComplexStrictConvexity 90. V. Lakshmikantham,TrendsinTheoryandPracticeofNonlinearDifferentialEquations 91. H.L Manocha and J. B. Srivastava,AlgebraandItsApplications 92. D. V. Chudnovsky and G. V. Chudnovsky, Classical and Quantum Models and Arithmetic Problems 93. J. W. Longley, LeastSquaresComputationsUsingOrthogonalization Methods 94. L. P. de Alcantara,MathematicalLogicandFormalSystems 95. C. E. Aull,RingsofContinuous Functions 96. R. Chuaqui, Analysis,Geometry,andProbability 97. L. Fuchs and L. Salce,ModulesOverValuationDomains 98. P. Fischer and W. R. Smith,Chaos,Fractals,andDynamics 99. W. B. Powell and C. Tsinakis,OrderedAlgebraicStructures 100. G. M. Rassias and T. M. Rassias, Differential Geometry, Calculus of Variations, and Their Applications 101. R.-E. Hoffmann and K H. Hofmann,ContinuousLatticesandTheirApplications 102. J. H. Lightboume III and S. M. Rankin III,PhysicalMathematicsandNonlinearPartial Differential Equations 103. C. A. Baker and L M. Batten,FiniteGeometries 104. J. W. Brewer et al.,LinearSystemsOverCommutativeRings 105. C. McCrory and T. Shifrin,GeometryandTopology 106. D. W. Kueke et al.,MathematicalLogicandTheoreticalComputerScience 107. B.-L. Lin and S. Simons,NonlinearandConvexAnalysis 108. S. J. Lee,OperatorMethodsforOptimalControlProblems 109. V. Lakshmikantham,NonlinearAnalysisandApplications 110. S. F. McCormick,MultigridMethods 111. M. C. Tangora, ComputersinAlgebra 112. D. V. Chudnovsky and G. V. Chudnovsky,SearchTheory 113. D. V. Chudnovsky and R. D. Jenks,ComputerAlgebra 114. M. C. Tangora, ComputersinGeometryandTopology 115. P. Nelson et al.,TransportTheory,InvariantImbedding,andIntegralEquations 116. P. Clément et al.,SemigroupTheoryandApplications 117. J. Vinuesa, OrthogonalPolynomialsandTheirApplications 118. C. M. Dafermos et al, DifferentialEquations 119. E.O. Roxin,ModernOptimalControl 120. J. C. Diaz,MathematicsforLargeScaleComputing 121. P.S. MilojevicNonlinearFunctionalAnalysis 122. C. Sadosky,AnalysisandPartialDifferential Equations 123. R. M. Shortt,GeneralTopologyandApplications 124. R. Wong,AsymptoticandComputationalAnalysis 125. D. V. Chudnovsky and R. D. Jenks,ComputersinMathematics 126. W. D. Wallis et al.,CombinatorialDesignsandApplications 127. S. Elaydi,DifferentialEquations 128. G. Chen et al.,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. Anno et al.,MathematicalPopulationDynamics 132. S. Coen,GeometryandComplexVariables 133. J. A. Goldstein et al.,DifferentialEquationswithApplicationsinBiology,Physics,andEngineering 134. S. J. Andima et al.,GeneralTopologyandApplications 135. P Clément et ai, SemigroupTheoryandEvolutionEquations 136. K. Jarosz,FunctionSpaces 137. J. M. Bayod et al.,p-adicFunctionalAnalysis 138. G. A. Anastassiou,ApproximationTheory 139. R. S. Rees,Graphs,Matrices,andDesigns 140. G. Abrams et al.,MethodsinModuleTheory 141. G. L Mullen and P. J.-S. Shiue,FiniteFields,CodingTheory,andAdvances inCommunications andComputing 142. M. C. Joshi and A. V. Balakrishnan,MathematicalTheoryofControl 143. G. Komatsu and Y. Sakane,ComplexGeometry 144. /. J. Bakelman,GeometricAnalysisandNonlinearPartialDifferential Equations 145. T. Mabuchi and S. Mukai,EinsteinMetricsandYang-Mills Connections 146. L Fuchs and R. Gôbel,AbelianGroups 147. A. D. Pollington and W. Moran,NumberTheorywithanEmphasisontheMarkoffSpectrum 148. G. Dore et al.,DifferentialEquationsinBanachSpaces 149. T. West,ContinuumTheoryandDynamicalSystems 150. K. D. Bierstedtetal., FunctionalAnalysis 151. K.G. Fischer et al., ComputationalAlgebra 152. K. D. Elworthyetal., DifferentialEquations,DynamicalSystems,andControlScience 153. P.-J. Cahen, et al.,CommutativeRingTheory 154. S.C. Cooper and W. J. Thron,ContinuedFractionsandOrthogonal Functions 155. P. Clément andG. Lumer, EvolutionEquations,ControlTheory,andBiomathematics 156. M. Gyllenberg and L. Persson,Analysis,Algebra,andComputersinMathematical Research 157. W.O. Bray et al.,FourierAnalysis 158. J. Bergen and S. Montgomery,AdvancesinHopfAlgebras 159. A. R. Magid,Rings,Extensions,andCohomology 160. N. H. Pavel,OptimalControlofDifferential Equations 161. M. Ikawa,SpectralandScatteringTheory 162. X. Liu and D. Siegel,ComparisonMethodsandStabilityTheory 163. J.-P. Zolésio,BoundaryControlandVariation 164. M. Kriieketai, FiniteElement Methods 165. G. Da Prato and L. Tubaro, ControlofPartialDifferential Equations 166. E. Ballico,ProjectiveGeometrywithApplications 167. M. Costabelet ai, BoundaryValueProblemsandIntegralEquationsinNonsmooth Domains 168. G. Ferreyra, G. R. Goldstein, and F. Neubrander,EvolutionEquations 169. S. Huggett,TwistorTheory 170. H. Cook et ai, Continua 171. D. F. Anderson and D. E. Dobbs,Zero-DimensionalCommutative Rings 172. K. Jarosz,FunctionSpaces 173. V. Ancona et ai, ComplexAnalysisandGeometry 174. E. Casas,ControlofPartialDifferentialEquationsandApplications 175. N. Kalton et ai, InteractionBetweenFunctionalAnalysis,HarmonicAnalysis,andProbability 176. Z. Deng et ai, DifferentialEquationsandControlTheory 177. P. Marcellini et ai PartialDifferentialEquationsandApplications 178. A. Kartsatos,TheoryandApplicationsofNonlinearOperatorsofAccretiveandMonotoneType 179. M. Maruyama,ModuliofVectorBundles 180. A. Ursini and P. Aglianò,LogicandAlgebra 181. X. H. Cao et ai, Rings,Groups,andAlgebras 182. D. Arnold and R. M. Rangaswamy,AbelianGroupsandModules 183. S. R. Chakravarthy and A. S. Alfa,Matrix-AnalyticMethodsinStochasticModels 184. J. E. Andersen et al.,GeometryandPhysics 185. P.-J. Cahen et al., CommutativeRingTheory 186. J. A. Goldstein et al., 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. Hinton and P. W. Schaefer,Spectral Theory and Computational Methods of Sturm-Liouville Problems 192. W. H. Schikhofet ai, p-adicFunctionalAnalysis 193. S. Sertoz,AlgebraicGeometry 194. G. Caristi and E. Mitidieri,ReactionDiffusionSystems 195. A. V. Fiacco,MathematicalProgrammingwithDataPerturbations 196. M. Kfizek et al.,FiniteElement Methods:Superconvergence, Post-Processing,andA Posteriori Estimates 197. S. Caenepeel and A. Verschoren,Rings,HopfAlgebras,andBrauerGroups 198. V. Drensky et al.,MethodsinRingTheory 199. W. B. Jones and A. Sri Ranga,OrthogonalFunctions,MomentTheory,andContinuedFractions 200. P. E. Newstead,AlgebraicGeometry 201. D. Dikranjan and L Salce,AbelianGroups,ModuleTheory,andTopology 202. Z. Chen et al.,AdvancesinComputational Mathematics 203. X. Caicedo and C. H. Montenegro,Models,Algebras,andProofs 204. C. Y. Yildirim and S. A. Stepanov,NumberTheoryandItsApplications 205. D. E. Dobbs et al.,AdvancesinCommutativeRingTheory 206. F. Van Oystaeyen, CommutativeAlgebraandAlgebraicGeometry 207. J. Kakol et al.,p-adicFunctionalAnalysis 208. M. Boulagouaz and J.-P. Tignol,AlgebraandNumberTheory 209. S. Caenepeel and F. Van Oystaeyen,HopfAlgebrasandQuantumGroups 210. F Van Oystaeyen and M. Saorin, Interactions Between Ring Theory and Representations of Algebras 211. R. Costa et al.,NonassociativeAlgebraandItsApplications 212. T.-X. He,WaveletAnalysisandMultiresolution Methods 213. H. Hudzik and L Skrzypczak,FunctionSpaces: TheFifthConference 214. J. Kajiwara et al.,FiniteorInfiniteDimensionalComplexAnalysis 215. G. Lumerand L Weis,EvolutionEquationsandTheirApplicationsinPhysicalandLifeSciences 216. J. Cagnol et al., ShapeOptimizationandOptimalDesign 217. J. Herzog and G. Restuccia,GeometricandCombinatorialAspectsofCommutativeAlgebra 218. G Chen et al., ControlofNonlinearDistributedParameterSystems 219. F. Ali Mehmeti et al.,PartialDifferentialEquationsonMultistructures 220. D. D. Anderson and I. J. Papick,IdealTheoreticMethodsinCommutativeAlgebra 221. Á. Granja et al.,RingTheoryandAlgebraicGeometry Additional Volumes in Preparation ideal theoretic methods in commutative algebra in honor of James A. Huckaba's retirement edited by Daniel D. Anderson University of Iowa Iowa City, Iowa Ira J. Papick University of Missouri Columbia, Missouri Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 First issued in hardback 2019 © 2001 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works ISBN-13: 978-0-8247-0553-4 (pbk) ISBN-13: 978-1-138-40174-7 (hbk) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com!) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923,978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Preface The conference Ideal Theoretic Methods in Commutative Algebra was convened to honor Professor James A. Huckaba's retirement from the Mathematics Department at the University of Missouri-Columbia. This Proceedings consists of research papers presented at that conference, as well as other contributed manuscripts. The combined effort reflects the substantial work of 38 authors and sharply illustrates the diversity of this field of study. Jim received his Ph.D. in mathematics from the University of Iowa in 1967. In that same year he came to the University of Missouri, and from that point on, he was consistently one of the Department's most valued members. During his 32-year academic career, he published numerous research papers in highly regarded mathematics journals, and authored and co-authored two research-level books in commutative ring theory (Commutative Rings with Zero Divisors, Marcel Dekker, 1977; Prüfer Domains, Marcel Dekker, 1997). Jim's enthusiasm and success in research was clearly reflected in his distinguished classroom teaching. His abilities extended past the classroom to seminars and colloquia, where he inspired both students and faculty. In particular, he successfully directed six Ph.D. students in commutative algebra, namely: 1. James Hays, Reduction of Ideals in Commutative Rings, 1971; Paul A. Froeschl III, Chained Rings and Maximal Conductor Rings, 1974; George W. Hinkle, Generalized Kronecker Function Rings and the Ring R(X), 1975; James M. Keller, Topics in the Theory of Graded Rings, 1978; Thomas G. Lucas, The Annihilator Conditions Property (A) and (AC), 1983; Albert Dixon, A Polynomial Ring Localization, 1987. Jim Huckaba is a rare individual of intelligence and compassion, and his professional contributions and accomplishments signify a life of outstanding academic achievement. The enormous success of this conference and the eminent quality of these Proceedings is directly due to the exhilarating talks and superb contributed papers of our colleagues. We extend our sincere appreciation to all par- ticipants. We are also thankful to the University of Missouri Mathematics Department and its Chair, Elias Saab, for supporting, both financially and philosophically, the conference and the retirement banquet. Further recognition is extended to Daniel Lieman for his notable contributions to the organization of the conference and banquet. His efficient style, coupled with his careful attention to details, was greatly appreciated. We are especially grateful to Amy Jo Wright, Wendy Hodge, and Brenda Frazier (the exceptional secretarial staff of UMC Mathematics Department) for their professional assistance in the preparation and handling of the conference and banquet. It was a wonderful joy to work with such dedicated and diligent individuals. Additionally, we are deeply indebted to Brenda Frazier, an extremely talented technical typist, computer stylist, and photographer, for iii