An algebraic introduction to K-theoryBruce A. Magurn.

Includes bibliographies and index.

"The presentation is self-contained, with all the necessary background and proofs, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry.

The prerequisites are minimal: just a first semester of algebra (including Galois theory and modules over a principal ideal domain). No experience with homological algebra, analysis, geometry, number theory, or topology is assumed. The author has.

Selected topics can be used to construct a variety of one-semester courses; coverage of the entire text requires a full year."--Jacket.

Groups of Modules: K[subscript 0. -- Free Modules -- Bases -- Matrix Representations -- Absence of Dimension -- Projective Modules -- Direct Summands -- Summands of Free Modules -- Grothendieck Groups -- Semigroups of Isomorphism Classes -- Semigroups to Groups -- Grothendieck Groups -- Resolutions -- Stability for Projective Modules -- Adding Copies of R -- Stably Free Modules -- When Stably Free Modules Are Free -- Stable Rank -- Dimensions of a Ring -- Multiplying Modules -- Semirings -- Burnside Rings -- Tensor Products of Modules -- Change of Rings -- K[subscript 0. of Related Rings -- G[subscript 0. of Related Rings -- K[subscript 0. as a Functor -- The Jacobson Radical -- Localization -- Sources of K[subscript 0. -- Number Theory -- Algebraic Integers -- Dedekind Domains -- Ideal Class Groups -- Extensions and Norms -- K[subscript 0. and G[subscript 0. of Dedekind Domains -- Group Representation Theory -- Linear Representations -- Representing Finite Groups Over Fields -- Semisimple Rings -- Characters -- Groups of Matrices: K[subscript 1. -- Definition of K[subscript 1. -- Elementary Matrices -- Commutators and K[subscript 1.(R) -- Determinants -- The Bass K[subscript 1. of a Category -- Stability for K[subscript 1.(R) -- Surjective Stability -- Injective Stability -- Relative K[subscript 1. -- Congruence Subgroups of GL[subscript n](R) -- Congruence Subgroups of SL[subscript n](R) -- Mennicke Symbols -- Relations Among Matrices: K[subscript 2. -- K[subscript 2.(R) and Steinberg Symbols -- Definition and Properties of K[subscript 2.(R) -- Elements of St(R) and K[subscript 2.(R) -- Exact Sequences -- The Relative Sequence -- Excision and the Mayer-Vietoris Sequence -- The Localization Sequence -- Universal Algebras -- Presentation of Algebras -- Graded Rings -- The Tensor Algebra -- Symmetric and Exterior Algebras -- The Milnor Ring -- Tame Symbols -- Norms on Milnor K-Theory -- Matsumoto's Theorem -- Sources of K[subscript 2. -- Symbols in Arithmetic -- Hilbert Symbols -- Metric Completion of Fields -- The p-Adic Numbers and Quadratic Reciprocity -- Local Fields and Norm Residue Symbols -- Brauer Groups -- The Brauer Group of a Field -- Splitting Fields -- Twisted Group Rings -- The K[subscript 2. Connection -- A Sets, Classes, Functions -- Chain Conditions, Composition Series

COPYRIGHT NOT covered - Click this link to request copyright permission:

https://lib.ciu.edu/copyright-request-form