by Hyman Bass
Publisher: W. A. Benjamin 1968
Number of pages: 793
The algebraic K-theory presented here is, essentially, a part of general linear algebra. It is concerned with the structure theory of projective modules, and of their automorphism groups. Thus, it is a generalization, in the most naive sense, off the theorem asserting the existence and uniqueness of bases for vector spaces, and of the group theory of the general linear group over a field.
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by Ioannis P. Zois - arXiv
We present introductory lectures on K-Theory covering its basic three branches, namely topological, analytic and Higher Algebraic K-Theory. The skeleton of these notes was provided by the author's notes from a graduate summer school on K-Theory.
by Jacek Brodzki - arXiv
An exposition of K-theory and cyclic cohomology. It begins with examples of various situations in which the K-functor of Grothendieck appears naturally, including the topological and algebraic K-theory, K-theory of C*-algebras, and K-homology.
by Hyman Bass - Tata Institute of Fundamental Research
Topics: The exact sequence of algebraic K-theory; Categories of modules and their equivalences; The Brauer group of a commutative ring; The Brauer-Wall group of graded Azumaya algebras; The structure of the Clifford Functor.
by Charles Weibel - Rutgers
Algebraic K-theory is an important part of homological algebra. Contents: Projective Modules and Vector Bundles; The Grothendieck group K_0; K_1 and K_2 of a ring; Definitions of higher K-theory; The Fundamental Theorems of higher K-theory.