An Introduction to Noncommutative Noetherian Rings

An Introduction to Noncommutative Noetherian Rings

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Description

This introduction to noncommutative Noetherian rings is intended to be accessible to anyone with a basic background in algebra. It can be used as a first-year graduate text, or as a self-contained reference. The authors' pedagogic style, with much explanatory discussion and exercises integrated into the development, will be a valuable aid in this respect. The standard techniques in the area (rings of fractions, bimodules, Krull dimension, linked prime ideals) are introduced and applied to a variety of problems. A recurring emphasis is placed on prime ideals and injective modules.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 1139173685
  • 9781139173681

Table of contents

Introduction; Prologue; 1. A few Noetherian rings; 2. Prime ideals; 3. Semisimple modules, Artinian modules, and nonsingular modules; 4. Injective hulls; 5. Semisimple rings of fractions; 6. Modules over semiprime goldie rings; 7. Bimodules and affiliated prime ideals; 8. Fully bounded rings; 9. Rings of fractions; 10. Artinian quotient rings; 11. Links between prime ideals; 12. Rings satisfying the second layer condition; 13. Krull dimension; 14. Numbers of generators of modules; 15. Transcendental division algebras; Appendix.show more