Algebraic \(K\)-theory. (English) Zbl 0174.30302

Bass, Hyman

Mathematics Lecture Note Series. New York-Amsterdam: W. A. Benjamin, Inc. xv, 762 pp. $ 5.95 (1968).

Reviewer: Walter Vogel (Halle)

MSC:

19-02	Research exposition (monographs, survey articles) pertaining to \(K\)-theory
16E20	Grothendieck groups, \(K\)-theory, etc.
13D15	Grothendieck groups, \(K\)-theory and commutative rings
18F25	Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
19Axx	Grothendieck groups and \(K_0\)
19Bxx	Whitehead groups and \(K_1\)
19Cxx	Steinberg groups and \(K_2\)
19Fxx	\(K\)-theory in number theory
19Lxx	Topological \(K\)-theory

Keywords:

algebraic \(K\)-theory; \(K_0\); \(K_1\); \(K_2\); projective modules; Serre’s stability theorem; Cancellation theorem; non-stable structure theorems; Cohn’s theorem; Seshadri’s theorem; normal subgroups of GL(n, A); Mennicke symbol; reciprocity laws over Dedekind rings; Grothendieck groups; Whitehead groups; Mayer-Vietoris sequence; K-theory in abelian categories; Grothendieck’s fundamental theorem for \(K_0\)

Citations:

Zbl 0109.41601; Zbl 0174.05203; Zbl 0132.26804; Zbl 0097.35604; Zbl 0161.01507; Zbl 0157.08202