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