Stability of algebraic inverse systems, II: Purity and localization

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/pdf/des-categories-abeliennes-8nuw5te8li.pdf

Des catégories abéliennes

Rings with several objects

/pdf/a-torsion-theory-for-abelian-categories-5asiqzwtbm.pdf

A torsion theory for Abelian categories

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

Algebraic K-theory

The development of a general theory of rings of quotients may be said to have started with the construction by Johnson [1] of the maximal ring of quotients Qmax of a non-singular ring A. This was done before the theory of injective envelopes had become available, but it was later proved that Qmax could be used as an injective envelope of the ring A. The maximal ring of quotients of an arbitrary ring A was defined by Utumi [1] and studied by Findlay and Lambek [1]. In particular, Lambek [2] proved that it could be interpreted as the bicommutator of the injective envelope of A.

Stability of algebraic inverse systems, II: Purity and localization

References

Des catégories abéliennes

Rings with several objects

A torsion theory for Abelian categories

Algebraic K-theory

Rings and modules of quotients

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