Algebraic K-Theory

Algebraic K-Theory

by Richard G. Swan


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From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in 1967. They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis. The results on K-theory are mostly of a very general nature."

Product Details

ISBN-13: 9783540042457
Publisher: Springer Berlin Heidelberg
Publication date: 01/01/1968
Series: Lecture Notes in Mathematics , #76
Edition description: 1968
Pages: 264
Sales rank: 811,572
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Category Theory.- Quotient categories.- Definition of KO(A) and some examples.- Krull-Schmidt theorems and applications.- Definition of G(R) and examples.- The connection between KO(R) and GO(R).- Localization and relation between GO(R) and GO(RS).- KO of graded rings.- Spec (R) and H(R).- Picard group and the determinant.- Basic topological remarks.- Chain complexes and the nilpotence of of .- Serre's theorem.- Cancerllation theorems.- K1(A).- K2(R).- The exact sequence of Ki's.- Further results on K1 and K0.- Relations between algebraic and topological K theory.

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