Ring Theory
eBook - PDF

Ring Theory

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

  1. 396 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Ring Theory

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

About this book

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.

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Information

Publisher
Academic Press
Year
2014
Print ISBN
9780122913501
eBook ISBN
9781483274157
Topic
Mathematics
Subtopic
Algebra
Index
Mathematics

Table of contents

  1. Front Cover
  2. Ring Theory
  3. Copyright Page
  4. Table of Contents
  5. CONTRIBUTORS
  6. PREFACE
  7. CHAPTER 1. RESTRICTED SEMIPRIMARY RINGS
  8. CHAPTER 2. ALGEBRAS WITH HOCHSCHILD DIMENSION ≤ 1
  9. CHAPTER 3. HEREDITARILY AND COHEREDITARILY PROJECTIVE MODULES
  10. CHAPTER 4. LIFTING MODULES AND A THEOREM ON FINITE FREE RESOLUTIONS
  11. CHAPTER 5. ON THE AUTOMORPHISM SCHEMEOF A PURELY INSEPARABLE FIELD EXTENSION
  12. CHAPTER 6. GENERALIZED RATIONAL IDENTITIES
  13. CHAPTER 7. K2 OF POLYNOMIAL RINGS AND OF FREE ALGEBRAS
  14. CHAPTER 8. TRIVIAL EXTENSIONS OF ABELIAN CATEGORIES AND APPLICATIONS TO RINGS: AN EXPOSITORY ACCOUNT
  15. CHAPTER 9. HIGHER K-FUNCTORS
  16. CHAPTER 10. PROPERTIES OF THE IDEALISER
  17. CHAPTER 11. STRUCTURE AND CLASSIFICATION OF HEREDITARY NOETHERIAN PRIME RINGS
  18. CHAPTER 12. ON THE REPRESENTATION OF MODULESBY SHEAVES OF MODULES OF QUOTIENTS
  19. CHAPTER 13. SOME REMARKS ON RINGS WITH SOLVABLE UNITS
  20. CHAPTER 14. QUASI-SIMPLE MODULES AND WEAK TRANSITIVITY
  21. CHAPTER 15. PRIME RIGHT IDEALS AND RIGHT NOETHERIAN RINGS
  22. CHAPTER 16. QUOTIENT RINGS
  23. CHAPTER 17. ON THE IDENTITIES OF AZUMAYA ALGEBRAS
  24. CHAPTER 18. BETTI NUMBERS AND REFLEXIVE MODULES
  25. CHAPTER 19. IDEALIZER RINGS
  26. CHAPTER 20. PERFECT PROJECTORS AND PERFECT INJECTORS
  27. CHAPTER 21. LINEARLY COMPACT MODULES AND LOCAL MORITA DUALITY
  28. CHAPTER 22. IDEALS IN FINITELY-GENERATED PI-ALGEBRAS
  29. CHAPTER 23. INTRODUCTION TO GROUPS OF SIMPLE ALGEBRAS
  30. CHAPTER 24. MODULES OVER PIDs THAT ARE INJECTIVEOVER THEIR ENDOMORPHISM RINGS
  31. PROBLEMS

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