Algebraic K-Theory

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.