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1 Lecture Notes 1n Mathematics For information about Vols , please contact your bookseller or Springer-Verlag. Vol. 490: The Geometry of Metric and Linear Spaces. Proceedings Edited by L. M. Kelly. X, 244 pages Vol. 491: K. A. Broughan, Invariants for Real-Generated Uniform Topological and Algebraic Categories. X, 197 pages Vol. 492: lnfinitary Logic: In Memoriam Carol Karp. Edited by D. W. Kueker. VI, 206 pages Vol. 493: F. W. Kamber and P. Tondeur, Foliated Bundles and Characteristic Classes. XIII, 208 pages Vol. 494: A Cornea and G. Licea. Order and Potential Resolvent Families of Kernels. IV, 154 pages Vol. 495: A. Kerber, Representations of Permutation Groups II. V, 175 pages Vol. 496: L. H. Hodgkin and V. P. Snaith, Topics ink-theory. Two Independent Contributions. Ill, 294 pages Vol. 497: Analyse Harmonique sur les Groupes de Lie. Proceedings Edite par P. Eymard et al. VI, 710 pages Vol. 4g9: Model Theory and Algebra. A Memorial Tribute to Abraham Robinson. Edited by D. H. Saracino and V. B. Weispfenning. X, 463 pages Vol. 499: Logic Conference, Kiel Proceedings. Edited by G. H. MOiler, A. Oberschelp, and K. Potthoff. V, 651 pages Vol. 500: ProofTheory Symposion, Kiel1974. Proceedings. Edited by J. Diller and G. H. MOiler. VIII, 383 pages Vol. 501: Spline Functions, Karlsruhe Proceedings. Edited by K. BOhmer, G. Meinardus, and W. Schempp. VI, 421 pages. 1g76. Vol. 502: Janos Galambos, Representations of Real Numbers by Infinite Series. VI, 146 pages Vol. 503: Applications of Methods of Functional Analysis to Problems in Mechanics. Proceedings Edited by P. Germain and B. Nayroles. XIX, 531 pages Vol. 504: S. Lang and H. F. Trotter, Froben1us Distributions m GL2 -Extensions. Ill, 274 pages. 1g76. Vol. 505: Advances in Complex Function Theory. Proceedings 1973/74. Edited by W. E. Kirwan and L. Zalcman. VIII, 203 pages Vol. 506: Numerical Analysis, Dundee Proceedings. Edited by G. A. Watson. X, 201 pages Vol. 507: M. C. Reed, Abstract Non-Linear Wave Equations. VI, 128 pages Vol. 508: E. Seneta, Regularly Varying Functions. V, 112 pages Vol. 509: D. E. Blair, Contact Manifolds m Riemannian Geometry. VI, 146 pages Vol. 510: V. Poenaru, Singularites C"' en Presence de Symetrie. V, 174 pages Vol. 511: Seminaire de Probabilites X. Proceedings 1974/75. Edite par P. A. Meyer. VI, 593 pages Vol. 512: Spaces of Analytic Functions, Kristiansand, Norway Proceedings. Edited by 0. B. Bekken, B. K. 0ksendal, and A. Stray. VIII, 204 pages Vol. 513: R. B. Warfield, Jr. Nilpotent Groups. VIII, 115 pages Vol. 514: Serninaire Bourbaki vol. 1974n5. Exposes V, 276 pages Vol. 515: Backlund Transformations. Nashville, Tennessee Proceedings. Edited by R. M. Miura. VIII, 295 pages Vol. 516: M. L. Silverstein, Boundary Theory for Symmetric Markov Processes. XVI, 314 pages Vol. 517: S. Glasner, Proximal Flows. VIII, 153 pages Vol. 518: Seminaire de Theorie du Potential, Proceedings Paris Edite par F. Hirsch et G. Mokobodzki. VI, 275 pages Vol. 519: J. Schmets, Espaces de Fonctions Continues. XII, 150 pages Vol. 520: R. H. Farrell, Techniques of Multivariate Calculation. X, 337 pages Vol. 521: G. Cheri in, Model Theoretic Algebra - Selected Topics. IV, 234 pages Vol. 522: C. 0. Bloom and N. D. Kazarinoff, Short Wave Radiation Problems in Inhomogeneous Media: Asymptotic Solutions. V. 104 pages Vol. 523: S. A. Albeverio and R. J. Heegh-Krohn, Mathematical Theory of Feynman Path Integrals. IV, 139 pages Vol. 524: Seminaire Pierre Lelong (Analyse) Annee 1974/75. Edite par P. Lelong. V, 222 pages Vol. 525: Structural Stability, the Theory of Catastrophes, and Applications in the Sciences. Proceedings Edited by P. Hilton. VI, 408 pages Vol. 526: Probability in Banach Spaces. Proceedings Edited by A. Beck. VI, 290 pages Vol. 527: M. Denker, Ch. Grillenberger, and K. Sigmund, Ergodic Theory on Compact Spaces. IV, 360 pages Vol. 528: J. E. Humphreys, Ordinary and Modular Representations of Chevalley Groups. Ill, 127 pages Vol. 529: J. Grandell, Doubly Stochastic Poisson Processes. X, 234 pages Vol. 530: S. S. Gelbart, Weil's Representation and the Spectrum of the Metaplectic Group. VII, 140 pages Vol. 531: Y.-C. Wong, The Topology of Uniform Convergence on Order-Bounded Sets. VI, 163 pages Vol. 532: Thoorie Ergodique. Proceedings 1973/1974. Edite par J.-P. Conze and M.S. Keane. VIII, 227 pages Vol. 533: F. R. Cohen, T. J. Lad a, and J. P. May, The Homology of Iterated Loop Spaces. IX, 490 pages Vol. 534: C. Preston, Random Fields. V, 200 pages Vol. 535: Singularites d'applications Differentiables. Plans-sur-Sex Edite par 0. Burlet et F. Ronga. V, 253 pages Vol. 536: W. M. Schmidt, Equations over Finite Fields. An Elementary Approach. IX, 267 pages Vol. 537: Set Theory and Hierarchy Theory. Bierutowice, Poland A Memorial Tribute to Andrzej Maslowski. Edited by W. Marek, M. Srebrny and A. Zarach. XIII, 345 pages Vol. 538: G. Fischer, Complex Analytic Geometry. VII, 201 pages Vol. 539: A. Badrikian, J. F. C. Kingman et J. Kuelbs, Ecole d'ete de Probabilites de Saint Flour V Edite par P.-L. Hennequin. IX, 314 pages Vol. 540: Categorical Topology, Proceedings Edited by E. Binz and H. Herrlich. XV, 719 pages Vol. 541: Measure Theory, Oberwolfach Proceedings. Edited by A. Bellow and D. Ktilzow. XIV, 430 pages Vol. 542: D. A. Edwards and H. M. Hastings, Cech and Steenrod Homotopy Theories with Applications tq Geometric Topology. VII, 296 pages Vol. 543: Nonlinear Operators and the Calculus of Variations, Bruxelles Edited by J. P. Gossez, E. J. L.ami Doze, J. Mawhin, and L. Waelbroeck, VII, 237 pages Vol. 544: Robert P. Lang lands, On the Functional Equations Satisfied by Eisenstein Series. VII, 337 pages Vot. 545: Noncommutative Ring Theory. Kent State Edited by J. H. Cozzens and F. L. Sandomierski. V, 212 pages Vol. 546: K. Mahler, Lectures on Transcendental Numbers. Edited and Completed by B. Divis and W. J. Le Veque. XXI, 254 pages Vol. 547: A. Mukherjea and N. A. Tserpes, Measures on Topological Semigroups: Convolution Products and Random Walks. V, 197 pages Vol. 548: D. A. Hejhal, The Selberg Trace Formula for PSL (2,1R). Volume I. VI, 516 pages Vol. 549: Brauer Groups, Evanston Proceedings. Edited by D. Zelinsky. V, 187 pages Vol. 550: Proceedings of the Third Japan - USSR Symposium on Probability Theory. Edited by G. Maruyama and J. V. Prokhorov. VI, 722 pages continuation on page 245

2 Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann 700 Module Theory Papers and Problems from The Special Session Sponsored by The American Mathematical Society at The University of Washington Proceedings, Seattle, August 15-18,1977 Edited by Carl Faith and Sylvia Wiegand Springer-Verlag Berlin Heidelberg New York 1979

3 Editors Carl Faith Department of Mathematics Rutgers, The State University New Brunswick, New Jersey 08903/USA Sylvia Wiegand Department of Mathematics University of Nebraska Lincoln, Nebraska 68588/USA AMSSubjectClassifications(1970): 13A 15,13B20,13B99,13C10,13C15, 13005, 13F05, 13F15, 13F20, 13HlO, 16A08, 16A34, 16A52, 16A62, 16A64, 16A66, 18GXX. ISBN Springer-Verlag Berlin Heidelberg NewYork ISBN Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. by Springer-Verlag Berlin Heidelberg 1979 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/

4 "I am going to hang up the glove s next year" (Nathan Jacobson) DEDICATION The contributors and particpants of the Special Session dedicate this volume to Nathan Jacobson in admiration, and gratitude for showing us what to do in the ring (theory).

5 PREFACE The editors wish to thank the partie ipants and contributors for their splendid cooperation, and for their joie de vivre which rnade the Special Session so much fun. The senior editor has grouped the contributed papers along ideological lines whenever possible, although, like rnuch ideology, these are far-fetched in rriany cases. It therefore would serve no useful purpose to expose this here, but the reading is certainly better served this way than the old ABC way. One ought to rnention that Dr. J. T. Stafford appeared first in the prograitl, as a guest of the Society introduced by the senior editor, and that Dr. Warfield's paper just has to follow Stafford's. Et cetera.

6 LIST OF PARTICIPANTS AND CONTRIBUTORS G. Azumaya Indiana University Bloomington, IN J. Beachy Northern Illinois Univ. DeKalb, IL A. K. Boyle University of Wisconsin Milwaukee, WI V. Camillo University of Iowa Iowa City, IA C. Faith Rutgers University New Brunswick, NJ K. R. Fuller University of Iowa Iowa City, IA F. Hansen Universitat Bochum D Bochum M. Hochster University of Michigan Ann Arbor, MI L. S. Levy University of Wisconsin Madison, WI S. Mohamed Kuwait University Kuwait B. L. Osofsky Rutgers University New Brunswick, NJ Z. Papp George Mason University Fairfax, VA M. Smith University of Texas Austin, TX J. T. Stafford Brandeis University Waltham, MA M. L. Teply University of Florida Gainesville, FL R. Warfield, Jr. University of Washington Seattle, WA R. Wiegand University of Nebraska Lincoln, NB S. Wiegand University of Nebraska Lincoln, NB E. Matlis Northwestern University Evanston, IL 60201

7 TABLE OF CONTENTS Papers J. Toby STAFFORD: Cancellation for Nonprojective Modules 3 Robert B. WARFIELD, Jr.: Stable Generation of Modules 16 Goro AZUMAYA: Some Aspects of Fuller's Theorem. 34 John A BEACHY: On Inversive Localization Ann K. BOYLE and. Edmund H. FELLER Semicritical Modules and k-primitive Rings. 57 K.R. FULLER and A Note on Loewy Rings and Chain Conditions V.P. CAMILLO : on Primitive Ideals Saad MOHAMED and Bruno J. MULLER: Decompositions of Dual-Continuous Modules 87 Friedhelm HANSEN and Mark L. TEPLY On the Gabriel Dimension and Subidealizer Rings.. 95 Melvin HOCHSTER: Big and Small Cohen-Macaulay Modules 119 Roger WIEGAND: Rings of Bounded Module Type 143 Carl FAITH: Injective Quotient Rings of Commutative Rings 151 Zoltan PAPP: Spectrum, Topologies and Sheaves for Left Noetherian Rings 204 Problems John BEACHY: Fully left bounded left Noetherian rings Carl FAITH: Bounded prime rings, pseudo-frobenius rings, the Jacobson radical of a ring. 218 Melvin HOCHSTER: Commutative Noetherian local rings 224 Saad MOHAMED: Continuous and dual-continuous modules 226 Zoltan PAPP: Left stable left Noetherian rings 228

8 Martha SMITH: Finitely generated algebras over a field 229 J. Toby STAFFORD: Simple Noetherian rings 230 Mark TEPLY: Subidealizers. 232 x Robert B. WARFIELD, Jr.: Equivalence of matrices, prime rings, number of generators, stable spaces. 235

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