Algebraic K-theory
Swan, R. G.
Algebraic K-theory [electronic resource] / by R. G. Swan. - IV, 264 p. online resource. - Lecture Notes in Mathematics, 76 0075-8434 ; . - Lecture Notes in Mathematics, 76 .
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.
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.".
9783540359173
10.1007/BFb0080281 doi
Algebra.
Algebra.
QA150-272
512
Algebraic K-theory [electronic resource] / by R. G. Swan. - IV, 264 p. online resource. - Lecture Notes in Mathematics, 76 0075-8434 ; . - Lecture Notes in Mathematics, 76 .
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.
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.".
9783540359173
10.1007/BFb0080281 doi
Algebra.
Algebra.
QA150-272
512