 
Summary: A geometric introduction
to commutative algebra
by Enrique Arrondo(*)
Version of January 10, 2006
0. Introduction and preliminaries
1. Rings and ideals; the Nullstellensatz
2. Noetherian rings
3. Modules; primary decomposition
4. Rings and modules of fractions
5. Integral dependence and the generalized Nullstellensatz
6. Geometry on the spectrum of a ring
7. Local rings
These notes correspond to the course of Commutative Algebra that I started teaching
the academic year 2003/2004 at the Universidad Complutense de Madrid. Since I am
still teaching the course for a third year, the notes (which were incomplete) are suffering
continuous changes. I thank my students of each year for their patience and suggestions (I
have to thank very particularly to Pepe Higes for many corrections). In the unlikely event
that I will succeed in writing something sensible, my goal was to present a selfcontained
basic introduction to the main topics of commutative algebra, regarded from a geometric
point of view.
