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

Format:

Book

Author/Creator:

Milnor, John, author.

Series:

Annals of mathematics studies ; Number 72.

Annals of Mathematics Studies ; 243

Language:

English

Subjects (All):

Associative rings.

Abelian groups.

Functor theory.

Physical Description:

1 online resource (200 pages).

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

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.

Contents:

Frontmatter

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

Notes:

Includes index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400881796

140088179X

OCLC:

945482788