Inhaltsverzeichnis

I Rings
  1. Ring elements
  2. Ring homomorphisms and ideals
  3. Ring properties: principal ideal rings, Noetherian rings, and Bézout rings
  4. Domains
II Modules
  1. Module homomorphisms
  2. Module properties: Noetherian, f.g. and f.p.; free, projective, torsion-free
III Exact sequences
  1. Split exact sequences and projectivity
  2. Free resolutions
  3. Sylvester rings
IV Categories
  1. Functors and functorial morphisms
V Special functors
  1. The covariant Hom-functor
  2. The contravariant Hom-functor
  3. The tensor product
  4. Relations between Hom and tensor product
VI Localization
  1. Local rings
  2. Modules of fractions
  3. Local properties
  4. Geometric interpretation of localization
VII Fitting invariants
  1. Determinantal ideals
  2. Fitting ideals
  3. The ranks of a matrix
  4. Euler characteristic
VIII Dimension theory
  1. The height and the prime divisors of an ideal
  2. Geometric interpretation of prime decomposition
  3. Primary decomposition
  4. Associated primes
  5. The zero-divisors of a ring
  6. Modules of finite length
  7. Krull's principal ideal theorem
  8. Dimension theory of Noetherian rings