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



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Autore: Milnor John Visualizza persona
Titolo: Introduction to Algebraic K-Theory. (AM-72), Volume 72 / / John Milnor Visualizza cluster
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  Visualizza cluster
ISBN: 1-4008-8179-X
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910154752203321
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Serie: Annals of mathematics studies ; ; Number 72.