ENGLISH

Introduction to Algebraic K-Theory

By John Milnor

Book information

Publisher
Princeton University Press, University of Tokyo Press
Year
1971
ISBN
0691081018
Language
english
Format
PDF
Filesize
13 MB (14096130 bytes)
Series
Annals of Mathematics Studies 72
Pages
197\202
Topic
Mathematics Algebra
Time added
2022-12-02 11:18:07

Description

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

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