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

• Autore: Milnor John
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1972
• Descrizione fisica: 1 online resource (200 pages)
• Disciplina: 512/.4
• Soggetto topico: Associative rings; Abelian groups; Functor theory
• Soggetto non controllato: Abelian group; Absolute value; Addition; Algebraic K-theory; Algebraic equation; Algebraic integer; Banach algebra; Basis (linear algebra); Big O notation; Circle group; Coefficient; Commutative property; Commutative ring; Commutator; Complex number; Computation; Congruence subgroup; Coprime integers; Cyclic group; Dedekind domain; Direct limit; Direct proof; Direct sum; Discrete valuation; Division algebra; Division ring; Elementary matrix; Elliptic function; Exact sequence; Existential quantification; Exterior algebra; Factorization; Finite group; Free abelian group; Function (mathematics); Fundamental group; Galois extension; Galois group; General linear group; Group extension; Hausdorff space; Homological algebra; Homomorphism; Homotopy; Ideal (ring theory); Ideal class group; Identity element; Identity matrix; Integral domain; Invertible matrix; Isomorphism class; K-theory; Kummer theory; Lattice (group); Left inverse; Local field; Local ring; Mathematics; Matsumoto's theorem; Maximal ideal; Meromorphic function; Monomial; Natural number; Noetherian; Normal subgroup; Number theory; Open set; Picard group; Polynomial; Prime element; Prime ideal; Projective module; Quadratic form; Quaternion; Quotient ring; Rational number; Real number; Right inverse; Ring of integers; Root of unity; Schur multiplier; Scientific notation; Simple algebra; Special case; Special linear group; Subgroup; Summation; Surjective function; Tensor product; Theorem; Topological K-theory; Topological group; Topological space; Topology; Torsion group; Variable (mathematics); Vector space; Wedderburn's theorem; Weierstrass function; Whitehead torsion
• Note generali: Includes index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Introduction to Algebraic K-Theory. (AM-72), Volume 72
• ISBN: 1-4008-8179-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154752203321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 72.