Lecture 1: Affine Varieties

In this lecture we review some concepts already encountered in the course Advanced Algebra

• Affine varieties and the Zariski topology
• Hilbert's Nullstellensatz: the correspondence between algebraic varieties and radical ideals
• The coordinate ring of an affine variety

Literature: [G] Chapter 1 and beginning of Chapter 2.

Suggested exercises: [G] 1.20-1.23.

Remark:  In this course affine varieties are not necessarily irreducible! Pay attention when you compare with other textbooks!