Ring Theory : Proceedings of a Conference on Ring Theory Held in Park City, Utah, March 2–6, 1971

Ring Theory provides information pertinent to the fundamental aspects of ring theory. This book covers a variety of topics related to ring theory, including restricted semi-primary rings, finite free resolutions, generalized rational identities, quotient rings, idealizer rings, identities of Azumaya algebras, endomorphism rings, and some remarks on rings with solvable units. Organized into 24 chapters, this book begins with an overview of the characterization of restricted semi-primary rings. This text then examines the case where K is a Hensel ring and A is a separable algebra. Other chapters consider establishing the basic properties of the four classes of projective modules, with emphasis on the finitely generated case. This book discusses as well the non-finitely generated cases and studies infinitely generated projective modules. The final chapter deals with abelian groups G that are injective when viewed as modules over their endomorphism rings E(G). This book is a valuable resource for mathematicians. Content: Front Matter, Page iii Copyright, Page iv CONTRIBUTORS, Pages ix-x PREFACE, Page xi RESTRICTED SEMIPRIMARY RINGS, Pages 1-8, Efraim P. Armendariz, Kenneth E. Hummel ALGEBRAS WITH HOCHSCHILD DIMENSION ≤ 1, Pages 9-27, Goro Azumaya HEREDITARILY AND COHEREDITARILY PROJECTIVE MODULES, Pages 29-62, George M. Bergman LIFTING MODULES AND A THEOREM ON FINITE FREE RESOLUTIONS, Pages 63-74, David A. Buchsbaum, David Eisenbud ON THE AUTOMORPHISM SCHEME OF A PURELY INSEPARABLE FIELD EXTENSION, Pages 75-106, Stephen U. Chase GENERALIZED RATIONAL IDENTITIES, Pages 107-115, P.M. Cohn K2 OF POLYNOMIAL RINGS AND OF FREE ALGEBRAS, Pages 117-123, P.M. Cohn TRIVIAL EXTENSIONS OF ABELIAN CATEGORIES AND APPLICATIONS TO RINGS: AN EXPOSITORY ACCOUNT, Pages 125-151, R. Fossum, P. Griffith, I. Reiten HIGHER K-FUNCTORS, Pages 153-159, S.M. Gersten PROPERTIES OF THE IDEALISER, Pages 161-169, A.W. Goldie STRUCTURE AND CLASSIFICATION OF HEREDITARY NOETHERIAN PRIME RINGS, Pages 171-229, Arun Vinayak Jategaonkar ON THE REPRESENTATION OF MODULES BY SHEAVES OF MODULES OF QUOTIENTS, Pages 231-234, J. Lambek SOME REMARKS ON RINGS WITH SOLVABLE UNITS, Pages 235-240, Charles Lanski QUASI-SIMPLE MODULES AND WEAK TRANSITIVITY, Pages 241-249, A.C. Mewborn PRIME RIGHT IDEALS AND RIGHT NOETHERIAN RINGS, Pages 251-255, Gerhard O. Michler QUOTIENT RINGS, Pages 257-285, Kiiti Morita ON THE IDENTITIES OF AZUMAYA ALGEBRAS, Pages 287-295, C. Procesi BETTI NUMBERS AND REFLEXIVE MODULES, Pages 297-308, Mark Ramras IDEALIZER RINGS, Pages 309-317, J.C. Robson PERFECT PROJECTORS AND PERFECT INJECTORS, Pages 319-332, Edgar A. Rutter Jr. LINEARLY COMPACT MODULES AND LOCAL MORITA DUALITY, Pages 333-346, F.L. Sandomierski IDEALS IN FINITELY-GENERATED PI-ALGEBRAS, Pages 347-351, Lance W. Small INTRODUCTION TO GROUPS OF SIMPLE ALGEBRAS, Pages 353-362, Moss E. Sweedler MODULES OVER PIDs THAT ARE INJECTIVE OVER THEIR ENDOMORPHISM RINGS, Pages 363-372, Fred Richman, Elbert A. Walker PROBLEMS, Pages 373-381