TY  - BOOK
AU  - Magurn,Bruce A.
TI  - An algebraic introduction to K-theoryBruce A. Magurn
T2  - Encyclopedia of mathematics and its applications
SN  - 9781107089525
AV  - QA612 .A444 2002
PY  - 2002///
CY  - Cambridge, UK, New York
PB  - Cambridge University Press
KW  - K-theory
KW  - Electronic Books
N1  - 2; 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; 2; b
N2  - "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
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