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R. G. Swan

R. G. Swan

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 76)

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Table of contents (19 chapters)

Front Matter

Pages I-IV

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Category Theory
- R. G. Swan
Pages 1-40
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Quotient categories
- R. G. Swan
Pages 40-64
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Definition of K_O(A) and some examples
- R. G. Swan
Pages 65-75
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Krull-Schmidt theorems and applications
- R. G. Swan
Pages 75-92
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Definition of G(R) and examples
- R. G. Swan
Pages 92-100
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The connection between KO(R) and GO(R)
- R. G. Swan
Pages 100-109
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Localization and relation between GO(R) and GO(RS)
- R. G. Swan
Pages 109-124
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KO of graded rings
- R. G. Swan
Pages 124-131
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Spec (R) and H(R)
- R. G. Swan
Pages 132-145
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Picard group and the determinant
- R. G. Swan
Pages 146-155
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Basic topological remarks
- R. G. Swan
Pages 155-160
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Chain complexes and the nilpotence of of
- R. G. Swan
Pages 161-169
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Serre's theorem
- R. G. Swan
Pages 170-183
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Cancellation theorems
- R. G. Swan
Pages 183-193
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K₁(A)
- R. G. Swan
Pages 193-204
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K2(R)
- R. G. Swan
Pages 204-211
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The exact sequence of Ki's
- R. G. Swan
Pages 211-223
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Further results on K1 and K0
- R. G. Swan
Pages 224-247
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Relations between algebraic and topological K theory
- R. G. Swan
Pages 247-256
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Keywords

About this book

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."

Bibliographic Information

Book Title: Algebraic K-Theory
Authors: R. G. Swan
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0080281
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1968
Softcover ISBN: 978-3-540-04245-7Published: 16 December 1968
eBook ISBN: 978-3-540-35917-3Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IV, 264
Topics: Algebra

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Algebraic K-Theory