Introduction to Algebraic K-Theory. (AM-72), Volume 72
eBook - PDF

Introduction to Algebraic K-Theory. (AM-72), Volume 72

  1. 200 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Introduction to Algebraic K-Theory. (AM-72), Volume 72

Book details
Table of contents
Citations

About This Book

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ? an abelian group K0? or K1? respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

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Information

Publisher
Princeton University Press
Year
2016
ISBN
9781400881796
Topic
Mathematics
Subtopic
Algebra
Index
Mathematics

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. CONTENTS
  6. Preface and Guide to the Literature
  7. §1. Projective Modules and K0Λ
  8. §2. Constructing Projective Modules
  9. §3. The Whitehead Group K1Λ
  10. §4. The Exact Sequence Associated with an Ideal
  11. §5. Steinberg Groups and the Functor K2
  12. §6. Extending the Exact Sequences
  13. §7. The Case of a Commutative Banach Algebra
  14. §8. The Product K1Λ ⊗ K1Λ → K2Λ
  15. §9. Computations in the Steinberg Group
  16. §10. Computation of K2Z
  17. §11. Matsumoto’s Computation of K2 of a Field
  18. §12. Proof of Matsumoto’s Theorem
  19. §13. More about Dedekind Domains
  20. §14. The Transfer Homomorphism
  21. §15. Power Norm Residue Symbols
  22. §16. Number Fields
  23. Appendix — Continuous Steinberg Symbols
  24. Index