Lecture 2: Dimension Theory

We go over, without proof, Noether Normalization and see how this implies various results in commutative algebra.  Then we outline Krull dimension theory for commutative rings. Finally we are going go see the "geometric side" of dimension: we will define the dimension for irreducible varieties. We will show that this is always finite and compute the dimension of the affine space and of products of affine varieties.

Literature:

[G] Second half of chapter 2

For the commutative algebra part see

[Gca] Andreas Gathmann, Commutative algebra, (see here Download here) Chapter 11 and 12.

Suggested exercises: [G] 2.17–19, 2.22, 2.30, 2.33–36.